Written math(page 373-375 even numbers) 2)log2 n=-3 then n=2^8 4)log3 1/9= n/3 then n=-3 6)log3 27=3n+6 then n=-1 8)log1/2 n=-2 then n=4 10)log8 n=1/3 then n= 12log1/9 27=n then n=-3 14)log9 n=-1/2 then n=3^4 16)logx 9/4=-2/3 then x= 18)log3 1/27=n then n=-3 20)logx1/49=-2 then x=7 B) 22)log3 1/9=x then x=-3 24)log10 0.01=x then x=-2 26)log4 2=x then x=-1/2 28)log3 27=x then x=3 30)log5 1=x then x=0 32)log1/4 2=x then x=-1 34)log5 125=x then x=3 36)log216 36=x then x=2/3 38)log4 1/32=x then x=-4 40)log8 32=x then x=5/3
11 log base 3 of 4*x^2*y^5 log base 3 of 4 + log base 3 of x^2 + log base 3 of y^5 ►log base 3 of 4 + 2 log base 3 of x + 5 log base 3 of y*
12 log base 5 of 3y/4√2x log base 5 of 3 + log base 5 of y - log base 5 of 4√2 + log base 5 of 4√x log base 5 of 3 + log base 5 of y - log base 5 of [4√2]^1/4 + log base 5 of [4√x]^1/4 log base 5 of 3 + log base 5 of y - log base 5 of 2^1/4 + log base 5 of x^1/4 ►log base 5 of 3 + log base 5 of y - 1/4 log base 5 of 2 + 1/4 log base 5 of x*
13 log base 6 of 3√2y/x^2 log base 6 of 3√2y - log base 6 of 3√x^2 log base 6 of 3√2 + log base 6 3√y - log base 6 of 3√x^2 log base 6 of [3√2]^1/3 + log base 6 [3√y]^1/3 - log base 6 of [3√x^2]^1/3 log base 6 of 2^1/3 + log base 6 y^1/3 - log base 6 of (x^2)^1/3 1/3 log base 6 of 2 + 1/3 log base 6 y - 1/3 log base 6 of x^2 1/3 log base 6 of 2 + 1/3 log base 6 y - 1/3*2 log base 6 of x ►1/3 log base 6 of 2 + 1/3 log base 6 y - 2/3 log base 6 of x*
14 log base x of 5*a^3*b^2*c^4 log base x of 5 + log base x of a^3 + log base x of b^2 + log base x of c^4 ►log base x of 5 + 3 log base x of a + 2 log base x of b + 4 log base x of c*
15 log base x of 3√a^2*b^2/√c log base x of 3√a^2 + log base x of 3√b^2 - log base x of √c log base x of [3√a^2]^1/3 + log base x of [3√b^2]^1/3 - log base x of [√c]^1/2 log base x of (a^2)^13 + log base x of (b^2)^1/3 - log base x of c^1/2 1/3 log base x of a^2 + 1/3 log base x of b^2 - 1/2 log base x of c 1/3*2 log base x of a + 1/3*2 log base x of b - 1/2 log base x of c ►2/3 log base x of a + 2/3 log base x of b - 1/2 log base x of c*
16 log base a of x^3/5y log base a of x^3 - log base a of 5 + log base a of y ►3 log base a of x - log base a of 5 + log base a of y*
17 log base 10 of √2x/y log base 10 of √2x - log base 10 of √y log base 10 of √2 + log base 10 of √x - log base 10 of √y log base 10 of [√2]^1/2 + log base 10 of [√x]^1/2 - log base 10 of [√y]^1/2 log base 10 of 2^1/2 + log base 10 of x^1/2 - log base 10 of y^1/2 ►1/2 log base 10 of 2 + 1/2 log base 10 of x - 1/2 log base 10 of y*
18 log base 3 of √ac^2 /b log base 3 of √ac^2 - log base 3 of b log base 3 of √a + log base 3 of √c^2 - log base 3 of b log base 3 of [√a]^1/2 + log base 3 of [√c^2]^1/2 - log base 3 of b log base 3 of a ^1/2 + log base 3 of (c^2)^1/2 - log base 3 of b 1/2 log base 3 of a + 1/2 log base 3 of c^2 - log base 3 of b 1/2 log base 3 of a + 1/2*2 log base 3 of c - log base 3 of b 1/2 log base 3 of a + 2/2 log base 3 of c - log base 3 of b ►1/2 log base 3 of a + log base 3 of c - log base 3 of b*
19 log base 2 of 4√a^3*b^2*c /2 log base 2 of 4√a^3*b^2*c - log base 2 of 2 log base 2 of 4√a^3 + log base 2 of 4√b^2 + log base 2 of 4√c - log base 2 of 2 log base 2 of [4√a^3]^1/4 + log base 2 of [4√b^2]^1/4 + log base 2 of [4√c]^1/4 - log base 2 of 2 log base 2 of (a^3)^1/4 + log base 2 of (b^2)^1/4 + log base 2 of c^1/4 - log base 2 of 2 log base 2 of 1/4 a^3 + log base 2 of 1/4 b^2+ 1/4 log base 2 of c - log base 2 of 2 1/4*3 log base 2 of a + 1/4*2 log base 2 of b + 1/4 log base 2 of c - log base 2 of 2 3/4 log base 2 of a + 2/4 log base 2 of 2/4 b + 1/4 log base 2 of c - log base 2 of 2 ►3/4 log base 2 of a + log base 2 of 1/2 b + 1/4 log base 2 of c - log base 2 of 2*
20 log base 5 of (8x)^2 / 4√y^3 log base 5 of 8^2 + log base 5 of x^2 - log base 5 of 4√y^3 2 log base 5 of 8 + 2 log base 5 of x - log base 5 of [4√y^3]^1/4 2 log base 5 of 8 + 2 log base 5 of x - log base 5 of (y^3)^1/4 2 log base 5 of 8 + 2 log base 5 of x - 1/4 log base 5 of y^3 2 log base 5 of 8 + 2 log base 5 of x - 1/4*3 log base 5 of y ►2 log base 5 of 8 + 2 log base 5 of x - 3/4 log base 5 of y*
11.) log base 3 of 4*x^2*y^5 log base 3 of 4 + log base 3 of x^2 + log base 3 of y^5 log base 3 of 4 + 2 log base 3 of x + 5 log base 3 of y* 12.) log base 5 of 3y/4√2x log base 5 of 3 + log base 5 of y - log base 5 of 4√2 + log base 5 of 4√x log base 5 of 3 + log base 5 of y - log base 5 of [4√2]^1/4 + log base 5 of [4√x]^1/4 log base 5 of 3 + log base 5 of y - log base 5 of 2^1/4 + log base 5 of x^1/4 log base 5 of 3 + log base 5 of y - 1/4 log base 5 of 2 + 1/4 log base 5 of x* 13.) log base 6 of 3√2y/x^2 log base 6 of 3√2y - log base 6 of 3√x^2 log base 6 of 3√2 + log base 6 3√y - log base 6 of 3√x^2 log base 6 of [3√2]^1/3 + log base 6 [3√y]^1/3 - log base 6 of [3√x^2]^1/3 log base 6 of 2^1/3 + log base 6 y^1/3 - log base 6 of (x^2)^1/3 1/3 log base 6 of 2 + 1/3 log base 6 y - 1/3 log base 6 of x^2 1/3 log base 6 of 2 + 1/3 log base 6 y - 1/3*2 log base 6 of x 1/3 log base 6 of 2 + 1/3 log base 6 y - 2/3 log base 6 of x* 14.) log base x of 5*a^3*b^2*c^4 log base x of 5 + log base x of a^3 + log base x of b^2 + log base x of c^4 log base x of 5 + 3 log base x of a + 2 log base x of b + 4 log base x of c* 15.) log base x of 3√a^2*b^2/√c log base x of 3√a^2 + log base x of 3√b^2 - log base x of √c log base x of [3√a^2]^1/3 + log base x of [3√b^2]^1/3 - log base x of [√c]^1/2 log base x of (a^2)^13 + log base x of (b^2)^1/3 - log base x of c^1/2 1/3 log base x of a^2 + 1/3 log base x of b^2 - 1/2 log base x of c 1/3*2 log base x of a + 1/3*2 log base x of b - 1/2 log base x of c 2/3 log base x of a + 2/3 log base x of b - 1/2 log base x of c* 16.) log base a of x^3/5y log base a of x^3 - log base a of 5 + log base a of y 3 log base a of x - log base a of 5 + log base a of y* 17.) log base 10 of √2x/y log base 10 of √2x - log base 10 of √y log base 10 of √2 + log base 10 of √x - log base 10 of √y log base 10 of [√2]^1/2 + log base 10 of [√x]^1/2 - log base 10 of [√y]^1/2 log base 10 of 2^1/2 + log base 10 of x^1/2 - log base 10 of y^1/2 1/2 log base 10 of 2 + 1/2 log base 10 of x - 1/2 log base 10 of y* 18.) log base 3 of √ac^2 /b log base 3 of √ac^2 - log base 3 of b log base 3 of √a + log base 3 of √c^2 - log base 3 of b log base 3 of [√a]^1/2 + log base 3 of [√c^2]^1/2 - log base 3 of b log base 3 of a ^1/2 + log base 3 of (c^2)^1/2 - log base 3 of b 1/2 log base 3 of a + 1/2 log base 3 of c^2 - log base 3 of b 1/2 log base 3 of a + 1/2*2 log base 3 of c - log base 3 of b 1/2 log base 3 of a + 2/2 log base 3 of c - log base 3 of b 1/2 log base 3 of a + log base 3 of c - log base 3 of b* 19.) log base 2 of 4√a^3*b^2*c /2 log base 2 of 4√a^3*b^2*c - log base 2 of 2 log base 2 of 4√a^3 + log base 2 of 4√b^2 + log base 2 of 4√c - log base 2 of 2 log base 2 of [4√a^3]^1/4 + log base 2 of [4√b^2]^1/4 + log base 2 of [4√c]^1/4 - log base 2 of 2 log base 2 of (a^3)^1/4 + log base 2 of (b^2)^1/4 + log base 2 of c^1/4 - log base 2 of 2 log base 2 of 1/4 a^3 + log base 2 of 1/4 b^2+ 1/4 log base 2 of c - log base 2 of 2 1/4*3 log base 2 of a + 1/4*2 log base 2 of b + 1/4 log base 2 of c - log base 2 of 2 3/4 log base 2 of a + 2/4 log base 2 of 2/4 b + 1/4 log base 2 of c - log base 2 of 2 3/4 log base 2 of a + log base 2 of 1/2 b + 1/4 log base 2 of c - log base 2 of 2* 20.) log base 5 of (8x)^2 / 4√y^3 log base 5 of 8^2 + log base 5 of x^2 - log base 5 of 4√y^3 2 log base 5 of 8 + 2 log base 5 of x - log base 5 of [4√y^3]^1/4 2 log base 5 of 8 + 2 log base 5 of x - log base 5 of (y^3)^1/4 2 log base 5 of 8 + 2 log base 5 of x - 1/4 log base 5 of y^3 2 log base 5 of 8 + 2 log base 5 of x - 1/4*3 log base 5 of y 2 log base 5 of 8 + 2 log base 5 of x - 3/4 log base 5 of y
11. log3 4x^2 y^5 log base 3 of 4 + log base 3 of x^2 + log base 3 of y^5 ------log base 3 of 4 + 2 log base 3 of x + 5 log base 3 of y*
12. log base 5 of 3y/4√2x log base 5 of 3 + log base 5 of y - log base 5 of 4√2 + log base 5 of 4√x log base 5 of 3 + log base 5 of y - log base 5 of [4√2]^1/4 + log base 5 of [4√x]^1/4 log base 5 of 3 + log base 5 of y - log base 5 of 2^1/4 + log base 5 of x^1/4 ---------log base 5 of 3 + log base 5 of y - 1/4 log base 5 of 2 + 1/4 log base 5 of x*
13. log base 6 of 3√2y/x^2 log base 6 of 3√2y - log base 6 of 3√x^2 1/3 log base 6 of 2 + 1/3 log base 6 y - 1/3*2 log base 6 of x -------1/3 log base 6 of 2 + 1/3 log base 6 y - 2/3 log base 6 of x*
14. logx 5a^3 b^2 c^4 log base x of 5 + log base x of a^3 + log base x of b^2 + log base x of c^4 -----log base x of 5 + 3 log base x of a + 2 log base x of b + 4 log base x of c*
15. log base x of 3√a^2*b^2/√c log base x of 3√a^2 + log base x of 3√b^2 - log base x of √c 1/3 log base x of a^2 + 1/3 log base x of b^2 - 1/2 log base x of c 1/3*2 log base x of a + 1/3*2 log base x of b - 1/2 log base x of c -------2/3 log base x of a + 2/3 log base x of b - 1/2 log base x of c*
16. loga x^3/5y log base a of x^3 - log base a of 5 + log base a of y -----3 log base a of x - log base a of 5 + log base a of y*
17. log base 10 of √2x/y log base 10 of √2x - log base 10 of √y log base 10 of √2 + log base 10 of √x - log base 10 of √y log base 10 of [√2]^1/2 + log base 10 of [√x]^1/2 - log base 10 of [√y]^1/2 log base 10 of 2^1/2 + log base 10 of x^1/2 - log base 10 of y^1/2 -----1/2 log base 10 of 2 + 1/2 log base 10 of x - 1/2 log base 10 of y*
18. log base 3 of √ac^2 /b log base 3 of √ac^2 - log base 3 of b log base 3 of √a + log base 3 of √c^2 - log base 3 of b 1/2 log base 3 of a + 1/2*2 log base 3 of c - log base 3 of b 1/2 log base 3 of a + 2/2 log base 3 of c - log base 3 of b -------1/2 log base 3 of a + log base 3 of c - log base 3 of b*
19. log base 2 of 4√a^3*b^2*c /2 log base 2 of 4√a^3*b^2*c - log base 2 of 2 log base 2 of 4√a^3 + log base 2 of 4√b^2 + log base 2 of 4√c - log base 2 of 2 1/4*3 log base 2 of a + 1/4*2 log base 2 of b + 1/4 log base 2 of c - log base 2 of 2 3/4 log base 2 of a + 2/4 log base 2 of 2/4 b + 1/4 log base 2 of c - log base 2 of 2 -----3/4 log base 2 of a + log base 2 of 1/2 b + 1/4 log base 2 of c - log base 2 of 2*
20. log base 5 of (8x)^2 / 4√y^3 log base 5 of 8^2 + log base 5 of x^2 - log base 5 of 4√y^3 2 log base 5 of 8 + 2 log base 5 of x - 1/4 log base 5 of y^3 2 log base 5 of 8 + 2 log base 5 of x - 1/4*3 log base 5 of y ------2 log base 5 of 8 + 2 log base 5 of x - 3/4 log base 5 of y
When I experience difficulty in solving Math problems, I tend to complain and wonder about the use of Math in my life. Come to think of it, I realized that in life, there are lots of applications of Mathematical principles. In the morning, when I hear my alarm clock, I estimate how much time do I have to sleep a little longer. When I take a shower, I can think how much gallon of water do I consume and how many liters there are in the gallons of water that I consume. As I shampoo my hair, I think about how many times can I wash my hair with a 200ml bottle of shampoo and how long will my bar of soap last. At breakfast time, I have to watch my calorie intake because I’m watching my weight. On my way to school, I would watch the speedometer of our car and know the distance from our house to school and find out how much time does it take for me to travel. With all these preparations before coming to school, I have set my mood to attend my math class. I pay attention and do my best to understand the lessons that my teacher gives us and try to solve the problems as much as I can. I think Mathematical skills are needed in other subjects, most especially in Science, TLE and even Music. Of course, I should know how to average my scores in all my subjects so I’ll be aware of how my grades are. When I get home, I do my homework in Math. As I encounter difficult problems, I begin to ponder about the importance of Math in my life. I don’t even plan to take up engineering or other courses that require higher Mathematics. But I have to get a high grade in this subject. What then should I do to overcome this weakness in Math? Sometimes, I sleep really late because of it and cry over it but I need to be more persevering in order to at least reach my expectations if not to surpass it. Perhaps, I should begin to like it, and eventually enjoy it, and treat it like a game. I realized that my mind is exercised to solve difficult problems so that when I grow older, I will able to solve difficult problems in life.
Mathematics has always been a subject in school I really enjoyed even when it was hard. It is my favorite because I never have difficulty with it and always get good marks in tests.
My earliest memories of math are my second grade in elementary. Prior to this age, the memories of math I have are flashcards, and these tests my parents would make up for me to take while at home. It felt very rewarding every time I solved a problem correctly. From that day forward I have permanently put in my mind that math was easy. As time passed by my curiosity and desire to excel at new things have helped me develop a new love for math.
I was first introduce to algebra during my sixth grade because of the enrichment classes that our school gave us. I remember hearing rumors from the freshmen about the difficulties of algebra. Little did I know, I would love algebra in the future. A great part of the reason why I love algebra is because math is like a puzzle. For me, puzzles are exciting and challenging at the same time and I am a student who never turns her back on challenges. This is when I started believing that math is not just about finding the correct answer, but also the process of discovering.
While entering high school, math changed drastically. The high school math consisted of new terms, new formulas and new numbers that I have never seen before. It was overwhelming at first, but I was fortunate enough to have amazing teachers to guide me through them. As I continue my studies I have learned how every concept requires special attention and focus.
The wonderful thing about Mathematics is that, besides some formula, there is nothing else to remember. Every step in solving a problem is done logically. Other subjects such as History and Geography require a lot of memory work. Remembering dates and other facts is hard work compared with the ease and simplicity of mathematical reasoning.
To me, the skills you learn from Mathematics are very useful in your every day life. It is a study that shows you step-by-step methods to solve any mathematical equation. To understand math, not only do you need to know how to solve the problem step-by- step, but you also need to understand the reasons why you are solving it the way you are. Mathematics teaches us how we can come up with a solution to every problem. The only true thing I ever picked up from my math teachers was the enthusiasm to learn and the enthusiasm in “getting it”.
“Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.” -Albert Einstein
Whenever someone mentions the subject "Math", people usually react in a violent manner. A lot of students see it as the most difficult subject in school. Although I do agree. Math is quite difficult. It's not easy to learn one Math topic to another. Although for some professionals, it would just be a piece of cake. But these kinds of people are rare. Not everyone can appreciate Math the way they do.
In my opinion, Math is a vast subject. Like I've said, it's not easy to learn one topic to another. But if you try to understand it, it's actually very simple. Some solutions may be long, and some are very simple. Some topics need a bucket-load of formulas to memorize, and some only need a simple solution. Math, I believe, is complicated. Topics go from easy to difficult and back to becoming easy. It's like a cycle that never ends. But if you give enough effort to try and understand the lesson, no doubt that you'll get it in no time.
I honestly believe that Math and I have quite a complicated relationship. I love Math, and I try to understand it in any way I can. There are times when I just get it, and there are times when it's just too confusing. But when I give effort and time to listen to the lessons, we'll get along fine in the end. That's how I see Math :)
MATH AND I Throughout the high school years, every student has their own opinions about the subjects they like and dislike. This does not mean the literal meaning. It means that it is about their strengths and weaknesses when it comes to academics. These opinions often change throughout the time. There are certain standards in every individual in order to succeed this kind of high school life. “Mathematics is an essential part of every high school student’s education.” This quote says it all. It explains the subject Math in eleven words. Every student learns certain lessons in math that will carry with them through life. Each of these are building blocks to help shape who we become. As a math student, I feel math has taught me not only about addition, subtraction, division... But it has taught me thinking skills and problem solving that will take me further than just math class. There are times in which you have to decide which path you will take after high school, although every path is different and you will take the skills in which you have learned in math class to a different level. When I was young, I used to say “I hate math”, although this sentence did not last long. As I was growing up, I slowly understood what math really meant and how we can apply it in real life situations. I used to say that this has nothing to do with shopping or dancing and such and that I won’t need this in the future. For my other batchmates, these are hard, most especially when you are surrounded by your best friends. Concentration is obviously needed when it comes to this matter. The dedication that this class requires teaches every student concentration. The concentration on this one course will help high school students pursue their dreams while taking other courses to achieve this. Another major influence on a high school student’s math education is the teacher. A teacher is crucial to a student’s success. The ideal teacher knows several ways to explain a certain concept. Doc Ed is an example of an ideal teacher. Soon enough, I know that I will become successful because of math. I know that this will be a big help in my future. I just have to focus at this moment and I can’t be distracted by the things that will destroy my future.
Every student has their own strengths and weaknesses. Same goes for their own opinion regarding which subject do they like or dislike,but I would daresay that Math would be one of the most infamous subject for us students. Many would ask "wouldn't life be easier without Math?" but then I would say no. A famous mathematician once said that ""The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth" which basically means that Math is something that we humans have to understand for us to be able to know what's going on around us.
Math wasn't such a nightmare for me until I stepped into highschool, this is where everything went hard. I wouldn't say that I hate Math, it's just that I wasn't putting in much effort about it. This made me realize that we always have to put specific effort for such concepts.
I always stated that I wouldn't need Math when I grow up but I was quickly corrected by my own self and realized that Math is an essential part of our daily life. I may not see it but it is everywhere. The technologies that I use is the most perfect example for me. Such ideals made me realize that I need Math in my life,that there's nothing hard when you put special attention and focus into something that you're really eager to learn.
9/17/12 Math Homework pp.373-375 even nos.
ReplyDeleteA.
2.log2 n=-3
2^-3=n
Answer: n=1/8
4.log1/9=n/3
3^n/3=1/9
Answer: n=-3
6.log3 27=3n+6
3^3n+6=3^3
3n+6=3
3n=-3
Answer: n=1
8.log1/2 n=-2
1/2^-2=n
Answer: n=1/4
10.log8 n=1/3
8^1/3=n
Answer: n=-1/8
12.log1/9 27=n
1/9^n=27
Answer: n=-2
14.log9 n=-1/2
9^-1/2=n
Answer: n=1/9
16.logx 9/4=-2/3
x^-2/3=9/4
Answer: n=3/2
18.log3 1/27=n
3^n=1/27
Answer: n=-3
20.logx 1/49=-2
x^-2=1/49
Answer: n=1/7
B.
22.log3 1/9
3^x=1/9
3^-2=1/9
Answer: x=-2
24.log10 0.01
10^x=0.01
10^-3=0.01
Answer: x=-3
26.log4 2
4^x=2
2^1=2
Answer: x=1
28.log3 27
3^x=27
3^3=27
Answer: x=3
30.log5 1
5^x=1
Answer: x=0
32.log1/4 2
1/4^x=2
Answer: x=-1
34.log5 125
5^x=125
5^3=125
Answer: x=3
36.log216 36
216^x=36
Answer: x=1
38.log4 1/32
4^x=1/32
2^-5=1/32
Answer: x=-5
40.log2 32
8^x=32
8^4=32
Answer: x=4
C.
42.log2 64-log3 81-log1/3 81
log4 4^3-log3 3^4-log1/3 3^-4
3-4-(-4)
Answer: 3
44.log1/9 27-log8 32
-----------------
log4 1/64-log10 100
log3/9 3^-3-log8 8^4
--------------------
log4 4^-3-log10 10^2
-3-4
----= -7/-5
-3+2
Answer: 7/5
2. log base 2 of n=-3
ReplyDelete2^-3=n
►n=1/8
4. log base 3 of 1/9= n/3
3^n/3=1/9
3^n/3=3^-2
n/3=-2
►n= -6
6. log base 3 of 27=3n+6
3^[3n+6]=27
3^[3n+6]=3^3
3n+6=3
3n=-3
►n=-1
8. log base 1/2 of n= -2
1/2^-2= n
►n=4
10. log base 8 of n=1/3
8^1/3=n
►n=2
12. log base 1/9 of 27=n
1/9^n=27
3^-2n=3^3
-2n=3
►n= -3/2
14. log base 9 of n= -1/2
9^-1/2=n
►n=-3
16. log base x of 9/4=-2/3
x^-2/3=9/4
[x^-2/3=9/4]^-3/2
x=[9/4]^-3/2
x=3/2^-3
►x=8/27
18. log base 3 of 1/27=n
3^n=1/27
3^n=3^-3
►n= -3
20. log base x of 1/49=-2
x^-2=1/49
x^-2=7^-2
►x=7
22. log base 3 of 1/9
3^n=1/9
3^n=3^-2
►n= -2
24. log base 10 of .01
10^n=.01
►n= -2
26. log base 4 of 2
4^n=2
2^2n=2^1
2n=1
►n=1/2
28. log base 3 of 27
3^n=27
3^n=3^3
►n=3
30. log base 5=1
5^n=1
►n=0
32. log base 1/4 of 2
1/4^n=2
2^-2n=2
-2n=1
►n= -1/2
34. log base 5 of 125
5^n=125
5^n=5^3
►n=3
36. log base 216 of 36
216^n=36
6^3n=6^2
3n=2
►n=2/3
38. log base 4 of 1/32
4^n=1/32
2^2n=2^-5
2n=-5
►n= -5/2
40. log base 8 of 32
8^n=32
2^3n=2^5
3n=5
►n=5/3
42. [log base 4 of 64]-[log base 3 of 81]-[log base 1/3 of 81]
3-4-[-4]
►3
44.[log base 1/9 of 27-log base 8 of 32]/[log base 4 of 1/64-log base 10 of 100]
{[-3/2]-[5/3]}/{[-3]-[2]}
[-16/6]/-5
[-8/3]/-5
[-8/3][-1/5]
►8/15
Homework for today
ReplyDeleteEVEN #'s
A.
#2.) log2n = -3
n = 1/8
#4.) log3(1/9) = n/3
= 3^(n/3) = 1/9
= n/3 = 1/9
= n/3 = -2/1
Answer n = -6
#6.) log3(27) = 3n+6
= log3^3n+6 = 27
= 3n+6 = 3
= 3n/3 = -6+3/3
Answer n = -1
#8.) log1/2n = -2
= 2^(-1)(-2) = n
Answer n = 2
#10.) log8n = 1/3
#12.) log1/9(27) = n
= 1/9n = 27
= 3^-2n = 3^3
= -2n/-2 = 3/-2
Answer: n = -3/2
#14.) log9n = -1/2
= 9^-1/2 = n
= 3^(2)(-1/2) = n
= 3^-1 = n
Answer: n = -1
#16.) logx(9/4) = -2/3
= x^-2/3 = 9/4
= (-2/3) = (9/4) *cross multiply*
Answer: x = -1
#20.) logx(1/49) = -2
= x^-2 = 1/49
= -2 = -2
Answer: x = 1
B.
#22.) log3(1/9) = x
= 3x = 1/9
= 3x = 3^-2
Answer: x = -2
#24.) log10(0.01) = x
= 10x = 10^-3
Answer: x = -3
#26.) log4(2) = x
= 4x = 2
= 2^2x = 1
= 2x/2 = 1/2
Answer: x = 1/2
#28.) log3(27) = x
= 3x = 27
= 3x = 3^3
Answer: x = 3
#30.) log5(1) = x
= 5x = 1
Answer: x = 1
#32.) log1/4(2) = x
= 1/4x = 2
= 2^-2x = 2
= -2x/-2 = 1/-2
Answer: x = -1/2
#34.) log5(125) = x
= 5x = 125
= 5x = 5^3
Answer: x =3
#36.) log216(36) = x
= 216x = 36
= 6^3x = 6^2
= 3x/3 = 2/3
Answer: x = 2/3
#38.) log4(1/32) = x
= 4x = 1/32
= 2^2x = 2^-5
= 2x/2 = -5/2
Answer: x = -5/2
#40.) log8(32) = x
= 8x = 32
= 2^3x = 2^5
= 3x/3 = 5/3
Answer: x = 5/3
C.
#42.) log4(64) - log3(81) - log(1/3)(81)
= log4(4^3) - log3(3^4) - log1/3(3^4)
= 3 - 4 - 4
Answer: -5
#44.) log1/9(27) - log8(32)/log81(1/64) - log10(100)
pp. 373-375
ReplyDeleteEven numbers.
log2 n = -3
2^-3 = n
n = 1/8
log3 1/9 =n/3
3^n/3 = 1/9
3^n/3 = 3^-2
n/3 = -2
[n/3 = -2]3
n = -6
log3 27 = 3n + 6
3^3n+6 = 27
3^3n+6 = 3^3
3n+6 = 3
3n = 3-6
[3n = 3-6]/3
n = 3-6/3
n = -3/3
n= -1
log1/2 n = -2
1/2^-2 = n
n = 4
log8 n = 1/3
8^1/3 = n
n = 1.9 or 19/10
log1/9 27 = n
1/9^n = 27
3^-2n = 3^3
-2n = 3
[-2n = 3]/-2
n = -3/2
log9 n= -1/2
9^-1/2 = n
n = 1/3
logx 9/4 = -2/3
x^-2/3 = 9/4
log3 1/27 = n
3^n = 1/27
n = -3
logx 1/49 = -2
x^-2 = 1/49
x = 7
log3 1/9
log3 1/9 = x
3^x = 1/9
x = -3
log10 0.01
log10 0.01 = x
10^x = 0.01
10^x = 10^-2
x = -2
log4 2
log4 2 = x
4^x = 2
2^2x = 2^1
2x = 1
[2x = 1]/2
x = 1/2
log3 27
log3 27 = x
3^x = 27
3^x = 3^3
x = 3
log5 1
log 5 1 = x
5^x = 1
x = 0
log1/4 2
log1/4 2 = x
1/4^x = 2
2^-2x = 2^1
-2x = 1
[-2x = 1]/-2
x= -1/2
log5 125
log5 125 = x
5^x = 125
5^x = 5^3
x = 3
log216 36
log 216 36 = x
216^x = 36
6^3x = 6^2
3x = 2
[3x = 2]/3
x = 2/3
log4 1/32
log 4 1/32 = x
4^x = 1/32
2^2x = 2^-5
2x = -5
[2x = -5]/2
x = -5/2
log8 32
log8 32 = x
8^x = 32
2^3x = 2^5
3x = 5
[3x = 5]/3
x = 5/3
log4 64 - log3 81 - log1/3 81
log4 64
log4 64 = x
4^x = 64
x = 3
log3 81
log3 81 = x
3^x = 81
x = 4
log1/3 81
log1/3 81 = x
1/3^x = 81
x = -4
3 - 4 - (-4)
= 3
log1/9 27
log1/9 27 = x
1/9^x = 27
3^-2x = 3^3
-2x = 3
[-2x = 3]/-2
x = -3/2
log8 32
log8 32 = x
8^x = 32
2^3x = 2^5
3x = 5
[3x = 5]/3
x = 5/3
log4 1/64
log4 1/64 = x
4^x = 1/64
x = -3
log10 100
log10 100 = x
10^x = 100
x = 2
-3/2 - 5/3/ -3 - 2
-9/6 - 10/6/ -5
-19/6/-5
= 19/30
Assignment
ReplyDeletepage 373-375 even nos.
the check mark (√) indicates the final answer
log2 n = -3
2^-3 = n
n = 1/8√
log3 1/9 =n/3
3^n/3 = 1/9
3^n/3 = 3^-2
n/3 = -2
[n/3 = -2]3
n = -6√
log3 27 = 3n + 6
3^3n+6 = 27
3^3n+6 = 3^3
3n+6 = 3
3n = 3-6
[3n = 3-6]/3
n = 3-6/3
n = -3/3
n= -1√
log1/2 n = -2
1/2^-2 = n
n = 4√
log8 n = 1/3
8^1/3 = n
n = 1.9 or 19/10√
log1/9 27 = n
1/9^n = 27
3^-2n = 3^3
-2n = 3
[-2n = 3]/-2
n = -3/2√
log9 n= -1/2
9^-1/2 = n
n = 1/3√
logx 9/4 = -2/3
x^-2/3 = 9/4
[x^-2/3 = 9/4]^-3/2
x = 9/4^-3/2
x = 0.3√
log3 1/27 = n
3^n = 1/27
n = -3√
logx 1/49 = -2
x^-2 = 1/49
x = 7√
log3 1/9
log3 1/9 = x
3^x = 1/9
x = -3√
log10 0.01
log10 0.01 = x
10^x = 0.01
10^x = 10^-2
x = -2√
log4 2
log4 2 = x
4^x = 2
2^2x = 2^1
2x = 1
[2x = 1]/2
x = 1/2√
log3 27
log3 27 = x
3^x = 27
3^x = 3^3
x = 3√
log5 1
log 5 1 = x
5^x = 1
x = 0√
log1/4 2
log1/4 2 = x
1/4^x = 2
2^-2x = 2^1
-2x = 1
[-2x = 1]/-2
x= -1/2√
log5 125
log5 125 = x
5^x = 125
5^x = 5^3
x = 3√
log216 36
log 216 36 = x
216^x = 36
6^3x = 6^2
3x = 2
[3x = 2]/3
x = 2/3√
log4 1/32
log 4 1/32 = x
4^x = 1/32
2^2x = 2^-5
2x = -5
[2x = -5]/2
x = -5/2√
log8 32
log8 32 = x
8^x = 32
2^3x = 2^5
3x = 5
[3x = 5]/3
x = 5/3√
log4 64 - log3 81 - log1/3 81
log4 64
log4 64 = x
4^x = 64
x = 3
log3 81
log3 81 = x
3^x = 81
x = 4
log1/3 81
log1/3 81 = x
1/3^x = 81
x = -4
3 - 4 - (-4)
= 3√
log1/9 27 - log8 32/ log4 1/64 - log10 100
log1/9 27
log1/9 27 = x
1/9^x = 27
3^-2x = 3^3
-2x = 3
[-2x = 3]/-2
x = -3/2
log8 32
log8 32 = x
8^x = 32
2^3x = 2^5
3x = 5
[3x = 5]/3
x = 5/3
log4 1/64
log4 1/64 = x
4^x = 1/64
x = -3
log10 100
log10 100 = x
10^x = 100
x = 2
-3/2 - 5/3/ -3 - 2
-9/6 - 10/6/ -5
-19/6/-5
= 19/30√
log2 n = -3
ReplyDelete2^-3 = n
n = 1/8
log3 1/9 =n/3
3^n/3 = 1/9
3^n/3 = 3^-2
n/3 = -2
[n/3 = -2]3
n = -6
log3 27 = 3n + 6
3^3n+6 = 27
3^3n+6 = 3^3
3n+6 = 3
3n = 3-6
[3n = 3-6]/3
n = 3-6/3
n = -3/3
n= -1
log1/2 n = -2
1/2^-2 = n
n = 4
log8 n = 1/3
8^1/3 = n
n = 1.9 or 19/10
log1/9 27 = n
1/9^n = 27
3^-2n = 3^3
-2n = 3
[-2n = 3]/-2
n = -3/2
log9 n= -1/2
9^-1/2 = n
n = 1/3
logx 9/4 = -2/3
x^-2/3 = 9/4
[x^-2/3 = 9/4]^-3/2
x = 9/4^-3/2
x = 0.3
log3 1/27 = n
3^n = 1/27
n = -3
logx 1/49 = -2
x^-2 = 1/49
x = 7
log3 1/9
log3 1/9 = x
3^x = 1/9
x = -3
log10 0.01
log10 0.01 = x
10^x = 0.01
10^x = 10^-2
x = -2
log4 2
log4 2 = x
4^x = 2
2^2x = 2^1
2x = 1
[2x = 1]/2
x = 1/2
log3 27
log3 27 = x
3^x = 27
3^x = 3^3
x = 3
log5 1
log 5 1 = x
5^x = 1
x = 0
log1/4 2
log1/4 2 = x
1/4^x = 2
2^-2x = 2^1
-2x = 1
[-2x = 1]/-2
x= -1/2
log5 125
log5 125 = x
5^x = 125
5^x = 5^3
x = 3
log216 36
log 216 36 = x
216^x = 36
6^3x = 6^2
3x = 2
[3x = 2]/3
x = 2/3
log4 1/32
log 4 1/32 = x
4^x = 1/32
2^2x = 2^-5
2x = -5
[2x = -5]/2
x = -5/2
log8 32
log8 32 = x
8^x = 32
2^3x = 2^5
3x = 5
[3x = 5]/3
x = 5/3
log4 64 - log3 81 - log1/3 81
log4 64
log4 64 = x
4^x = 64
x = 3
log3 81
log3 81 = x
3^x = 81
x = 4
log1/3 81
log1/3 81 = x
1/3^x = 81
x = -4
3 - 4 - (-4)
= 3
log1/9 27 - log8 32/ log4 1/64 - log10 100
log1/9 27
log1/9 27 = x
1/9^x = 27
3^-2x = 3^3
-2x = 3
[-2x = 3]/-2
x = -3/2
log8 32
log8 32 = x
8^x = 32
2^3x = 2^5
3x = 5
[3x = 5]/3
x = 5/3
log4 1/64
log4 1/64 = x
4^x = 1/64
x = -3
log10 100
log10 100 = x
10^x = 100
x = 2
-3/2 - 5/3/ -3 - 2
-9/6 - 10/6/ -5
-19/6/-5
= 19/30
Edgar Caballero 10-pascal
ReplyDelete#2
2^-3=n
n=1/8
#8
1/0^-2=n
n=4
#10
8^1/3=n
n=2.66 or 2/2/3
#14
9^-1/2=n
n=.333
#18
3^n=1/27
n=-3
#20
x^-2=1/49
x=7
#22
3^x=1/9
x=-2
#24
10^x=.01
x=-2
#26
4^x=2
x=1/2
#28
3^x=27
x=3
#30
5^x=1
x=0
#32
1/4^x=2
x=-1/2
#34
5^x=125
x=3
#42
4^x=64
=3
3^x=81
=4
1/3^81
=-4
3-4-(-4)
=3
#44
1/9^x=27
3^-2x=3^3
x=-3/2
8^x=32
2^3x=2^5
x=5/3
4^x=1/64
x=-3
10^x=100
x=2
(-3/2-5/3)/(-3-2)
=1/7/12 or1.58
Math Homework for September 17, 2012
ReplyDeletep. 373-375; Even numbers
A.
2) log2 n = -3
2^-3 = n
1/8 = n
ANSWER: n = 1/8
4) log3 1/9 = n/3
3^n/3 = 1/9
3^n/3 = 3^-2
n/3 = -2/1
n = -6
ANSWER: n = -6
6) log3 27 = 3n+6
3^3n+6 = 27
3^3n+6 = 3^3
3n+6 = 3
3n = 3-6
3n/3 = -3/3
n = -1
ANSWER: n = -1
8) log1/2 n = -2
1/2^-2 = n
4 = n
ANSWER: n = 4
10) log8 n = 1/3
8^1/3 = n
cube root of 8 = n
2 = n
ANSWER: n = 2
12) log1/9 27 = n
1/9^n = 27
3^-2n = 3^3
-2n/-2 = 3/-2
3/-2 = n
ANSWER: n = -3/2
14) log9 n = -1/2
9^-1/2 = n
square root of 1/9 = n
1/3 = n
ANSWER: 1/3
18) log3 1/27 = n
3^n = 1/27
3^n = 3^-3
n = -3
ANSWER: -3
20) logx 1/49 = -2
x^2 = 1/49
x = - square root of 1/49
x = 7
ANSWER: x= 7
B.
22) log3 1/9
log3 1/9 = x
3^x = 1/9
3^x = 3^-2
x = -2
ANSWER: x = -2
24) log10 0.01
log10 0.01 = x
10^x = 0.01
10^x = 10^-2
x = -2
ANSWER: x = -2
26) log4 2
log4 2 = x
4^x = 2
2^2x = 2^1
2x = 1
2x/2 = 1/2
x = 1/2
ANSWER: x = 1/2
28) log3 27
log3 27 = x
3^x = 27
3^x = 3^3
x = 3
ANSWER: x = 3
30) log5 1
log5 1 = x
5^x = 1
5^0x = 1
0x = 1
ANSWER = 0
32) log1/4 2
log1/4 2 = x
1/4^x = 2
2^-2x = 2^1
-2x = 1
-2x/-2 = 1/-2
x = 1/-2
ANSWER: -1/2
34) log5 125
log5 125 = x
5^x = 125
5^x = 5^3
x = 3
ANSWER: x = 3
36) log216 36
log216 36 = x
216^x = 36
6^3x = 6^2
3x = 2
3x/3 = 2/3
x = 2/3
ANSWER: x = 2/3
38) log4 1/32
log4 1/32 = x
4^x = 1/32
2^2x = 2^-5
2x = -5
2x/2 = -5/2
x = -5/2
ANSWER: -5/2
40) log8 32
log8 32 = x
8^x = 32
2^3x = 2^5
3x = 5
3x/3 = 5/3
x = 5/3
ANSWER: 5/3
C.
42) log4 64 - log3 81 - log1/3 81
= log4 4^3 - log3 3^4 - log1/3 1/3^-4
= 3 - 4 - (-4)
= -3
ANSWER: -3
44) (log1/9 27 - log8 32)/(log4 64 - log10 100)
= (log1/9 1/9^-3/2 - log8 8^5/3)/(log4 4^-3 - log10 10^2)
= (-3/2 - 5/3)/(-3-2)
= (-19/6)/(-5/1)
= -19/6 * -1/5
= -19/30
ANSWER: -19/30
41) log10 0.01
ReplyDeletelet x= = log10 0.01
10x=0.01
10x=10-2
x=-2
log2 1/16
let x=log2 1/16
2x=2-4
x= -4
log3 27
let x= log3 27
3x=27
3x=3(3)
x=3
fa= -2+(-4)-3= -9
42) log4 64 - log3 81 - log1/3 81
let x= log4 64
4x=4(3)
x=3
log3 81
let x= log3 81
3x=81
3x=3(4)
x=4
log1/3 81
let x3 = log 1/3 81
1/3x=81
1/3x=1/3-4
x= -4
fa= 3-4-(4)=3
43)log4 1/16 - log16 4
log81 3 - log9 27
log4 1/16
let x = log4 1/16
4x=1/16
4x=4-2
x= -2
log16 (4)
let x = log16 4
16x= 4
16x= 161/2
x = 1/2
log81 (3)
81x=3
81x= 81 1/4
x=1/4
log9 (27)
let x = log9(27)
9x=27
9x=9 3/2
x=3/2
fa= -2 - 1/2 = - (5/2)
1/4 - 3/2 = - (5/4)
x=2
44) log 1/9 (27) - log8 (32)
log4 1/64 - log10 (100)
log 1/9 (27)
let x = log 1/9 (27)
1/9x = 27
1/9x = 1/9 -(2/3)
x= 3/2
log8= 32
let x = log8 (32)
8x=32
8x= 8 (5/3)
x=(5/3)
log4 1/64
let x = log 4 (1/64)
4x= 1/64
4x= 4(-3)
x= -3
log10 (100)
let x = log10 (100)
10x=100
10x= 10(2)
x=2
fa= -(2/3) - (5/3)
-3 - 2
= (19/6) - 5 = 19/30
Written math(page 373-375 even numbers)
ReplyDelete2)log2 n=-3 then n=2^8
4)log3 1/9= n/3 then n=-3
6)log3 27=3n+6 then n=-1
8)log1/2 n=-2 then n=4
10)log8 n=1/3 then n=
12log1/9 27=n then n=-3
14)log9 n=-1/2 then n=3^4
16)logx 9/4=-2/3 then x=
18)log3 1/27=n then n=-3
20)logx1/49=-2 then x=7
B)
22)log3 1/9=x then x=-3
24)log10 0.01=x then x=-2
26)log4 2=x then x=-1/2
28)log3 27=x then x=3
30)log5 1=x then x=0
32)log1/4 2=x then x=-1
34)log5 125=x then x=3
36)log216 36=x then x=2/3
38)log4 1/32=x then x=-4
40)log8 32=x then x=5/3
Mika Lapus
ReplyDeleteSeptember 17, 2012
Pages 373 – 375 all even numbers (written math)
*♦ = final answer
2.) Log2 n = -3
2^-3 = n
½^3 = n
1/8 = n ♦
4.) log3 1/9 = n/3
3^n/3 = 1/9
3^n/3 = 3^-2
n/3 = -2
n= -6 ♦
6.) log3 27 = 3n+6
3^3n+6 = 27
3^3n+6 = 3^3
3n = 3 – 6
3n = -3 (all over 3)
n = -1 ♦
8.) log1/2 n = -2
½^-2 = n
n = 4 ♦
10.) log8 n = 1/3
8^1/3 = n
(cube root of 8) = n
2 = n ♦
12.) log1/9 27 = n
1/9^n = 27
3^-2n = 3^3
-2n = 3 (all over -2)
n = 3/-2 ♦
14.)log9n = -1/2
9^ - ½ = n
n = 1/3 ♦
16.) logx 9/4 = -2/3
x^-2/3 = 9/4
[x^-2/3 = 9/4]^-3/2
x = 9/4^-3/2
x = 0.3 ♦
18.) log3 1/27 = n
3^n = 1/27
3^n = 3^-3
n = -3 ♦
20.) logx 1/49 = -2
X^-2 = 1/49
x^-2 = 7^ -2
-2 = -2
X = 7 ♦
LETTER B
22.) x = log3 1/9
3^x = 1/9
3^x = 3^-2
X = -2
Log3 1/9 = -2 ♦
24.) log10 0.01 = x
10^x = 0.01
10^x = 10^-2
X = -2
Log10 0.01 = -2 ♦
26.) log4 2 = x
4^x = 2
2^2x = 2^1
2x = 1 (all over 2)
X =1/2
Log4 2 = 1/2 ♦
28.) log3 27 = x
3^x = 27
3^x = 3^3
X = 3
Log3 27 = 3 ♦
30.) log5 1 = x
5^x = 1
5^x = 5^0
X = 0
Log5 1 = 0 ♦
32.) log1/4 2 = x
1/4 ^ x = 2
2^-2x = 2^1
-2x = 1 (all over -2)
X = 1/-2
Log1/4 2 = 1/-2 ♦
34.) log5 125 = x
5^x = 125
5^x = 5^3
X = 3
Log5 125 = 3 ♦
36.) log216 36 = x
216^x = 36
6^3x = 6^2
3x = 2 (all over 3)
X = 2/3
Log216 36 = 2/3 ♦
38.) log4 1/32 = x
4^x = 1/32
2^2x = 2^-5
2x = -5 (all over 2)
X = -5/2
Log4 1/32 = -5/2 ♦
40.) log8 32 = x
8^x = 32
2^3x = 2^5
3x = 5 (all over 3)
X = 5/3
Log8 32 = 5/3 ♦
Letter C
42.) log4 64 – log3 81 – log1/3 81
log4 4^3 - log3 3^4 - log1/3 1/3^-4
3 - 4 - (-4)
= 3 ♦
44.) (log1/9 27 – log8 32) \ (log4 1/64 – log10 100)
(3/-2 – 5/3) / (-3-2)
(9 + 10) / -5
= 19/5 ♦
42.) log4 64 - log3 81 - log1/3 81
ReplyDeletelog4 4^3 - log3 3^3 -log1/3 3^3
=3-3-3
=-3
44.) log1/9 27 - log8 32
______________________________________
log4 1/64 - log10 1000
log1/9 3^2 - log8 2^4
______________________________________
log4 4^3 - log10 10^3
2-4
____________
3-3
=-2
_____
0
Homework: Written Math pp. 373-375 even #'s.
ReplyDeleteA. Solve for n.
Solutions:
#2 2^-3 = n
n = 1/8 ✓
#4 3^n/3 = 1/9
3^n/3 = 3^-3
n = -9 ✓
#6 3^3n+6 = 27
3^3n+6 = 3^3
3n+6 = 3
3n = -3
n = -1 ✓
#8 1/2^-2 = n
2^2 = n
n = 4 ✓
#10 8^1/3 = n
³√8 = n
n = 2 ✓
#12 1/9^n = 27
3^-2n = 3^3
-2n = 3
n = -3/2 ✓
#14 9^-1/2 = n
√9 = n
1/√9 = n
n = 1/3 ✓
#16 x^-2/3 = 9/4
[x^-2/3 = 9/4]^-3/2
[x^-2/3]^-3/2
[√9/√4]^3
x = 8/27 ✓
#18 3^n = 1/27
3^n = 3^-3
n = -3 ✓
#20 x^-2 = 1/49
x^-2 = 7^-2
x = 7 ✓
B. Evaluate the following.
#22 3^x = 1/9
3^x = 3^-2
x = -2 ✓
#24 10^x = 0.01
10^x = 1/100
10^x = 10^-2
x = -2 ✓
#26 4^x = 2
2^2x = 2
2x = 1
x = 1/2 ✓
#28 3^x= 27
3^x = 3^3
x = 3 ✓
#30 5^x = 1
x = 1 ✓
#32 1/4^x = 2
2^-2x = 2
-2x = 1
x = -1/2 ✓
#34 5^x = 125
5^x = 5^3
x = 3 ✓
#36 216^x = 36
6^3x = 6^2
3x = 2
x = 2/3 ✓
#38 4^x = 1/32
2^2x = 2^-5
2x = - 5
x = -5/2 ✓
#40 8^x = 32
2^3x = 2^5
3x = 5
x = 5/3 ✓
C. Evaluate each numerical expression.
#42 4^x=64 - 3^x=81 - 1/3^x=81
x=3 - x=4 - x=-4
3 - 4 - (-4)
x = 3 ✓
#44 [1/9^x=27 - 8^x=32] / [4^x=1/64 - 10^x=100]
[3^-2x=3^3- 2^3x=3^5] / [4^x=4^-3 - 10^x=10^2]
[x=-3/2 - x=5/3] / [x=-3 - x=2]
[-3/2 - 5/3] / [-3 - 2]
LCD: 6 [-3/2 - 5/3] / -5
-19/6 / -1/5
x = 19/30 ✓
#2 log2 n =-3
ReplyDeleten=1/8
#4 log3 1/9=n/3
n=-6
#6 log3 27 =3n+6
n=-1
#8 log1/2 n = -2
n=4
#10 log8 n = 1/3
n=8/3
#12 log1/9 27 = n
n=-2
#14 log9 n = -1/2
n=1/3
#16 logx 9/4 = -2/3
x=1
#18 log3 1/27 = n
n=-3
#20 logx 1/49 = -2
x=7
#22 log3 1/9
x=-2
#24 log10 0.01
x=-2
#26 log4 2
x=1/2
#28 log3 27
x=27
#30 log5 1
x=1
#32 log1/4 2
x=-1
#34 log5 125
x=3
#36 log216 36
x=2/3
#38 log4 1/32
x=-5/2
#40 log8 32
x=3/5
Homework for September 17, 2012.
ReplyDeleteA.
#2. 2^-3 = n
[n = 1/8]
#4. 3^n/3 = 1/9
3^n/3 = 3^-2
[n = -6]
#6. 3^3n+6 = 27
3^3n+6 = 3^3
3n+6 = 3
3n = 3-6
3n = -3
[n = -1]
#8. 1/2^-2 = n
[n = 1/4]
#10. 8^1/3 = n
[n = 2]
#12. 1/9^n = 27
3^-2n = 3^3
-2n = 3
[n = -3/2]
#14. 9^-1/2 = n
[n = 1/3]
#18. 3^n = 1/27
3^n = 3^-3
[n = -3]
B.
#22. log3 1/9 = x
3^x = 1/9
3^x = 3^-3
[x = -3]
#24. log10 0.01 = x
10^x = 0.01
10^x = 10^-2
[x = -2]
#26. log4 2 = x
4^x = 2
2^2x = 2
2x = 1
[x = 1/2]
#28. log3 27 = x
3^x = 27
3^x = 3^3
[x = 3]
#30. log5 1 = x
5^x = 1
x = 1
#32. log1/4 2 = x
1/4^x = 2
2^-2x = 2
-2x = 1
[x = -1/2]
#34. log5 125 = x
5^x = 125
5^x = 5^3
[x = 3]
#36. log216 36 = x
216^x = 36
6^3x = 6^2
3x = 2
[x = 2/3]
#38. log4 1/32 = x
4^x = 1/32
2^2x = 2^-5
2x = -5
[x = -5/2]
#40. log8 32 = x
8^x = 32
2^3x = 2^5
3x = 5
[x = 5/3]
C.
#42. log4 2^6 - log3 3^4 - log1/3 3^4
6 - 4 - 4
[-2]
#44. log1/9 3^3 - log8 2^5
---------------------
log4 2^-6 - log10 10^2
3 - 5
-----
6 - 2
-2
--
-8
[1/4]
A.
ReplyDelete2. log2n = -3
A: n = 1/8
4. log3(1/9) = n/3
= 3^(n/3) = 1/9
= n/3 = 1/9
= n/3 = -2/1
A: n = -6
6. log3(27) = 3n+6
= log3^3n+6 = 27
= 3n+6 = 3
= 3n/3 = -6+3/3
A: n = -1
8. log1/2n = -2
= 2^(-1)(-2) = n
A: n = 2
10. log8n = 1/3
12. log1/9(27) = n
= 1/9n = 27
= 3^-2n = 3^3
= -2n/-2 = 3/-2
A: n = -3/2
14. log9n = -1/2
= 9^-1/2 = n
= 3^(2)(-1/2) = n
= 3^-1 = n
A: n = -1
16. logx(9/4) = -2/3
= x^-2/3 = 9/4
= (-2/3) = (9/4) *cross multiply*
A: x = -1
20. logx(1/49) = -2
= x^-2 = 1/49
= -2 = -2
A: x = 1
B.
22. log3(1/9) = x
= 3x = 1/9
= 3x = 3^-2
A: x = -2
24. log10(0.01) = x
= 10x = 10^-3
A: x = -3
26. log4(2) = x
= 4x = 2
= 2^2x = 1
= 2x/2 = 1/2
A: x = 1/2
28. log3(27) = x
= 3x = 27
= 3x = 3^3
A: x = 3
30. log5(1) = x
= 5x = 1
A: x = 1
32. log1/4(2) = x
= 1/4x = 2
= 2^-2x = 2
= -2x/-2 = 1/-2
A: x = -1/2
34. log5(125) = x
= 5x = 125
= 5x = 5^3
A: x =3
36. log216(36) = x
= 216x = 36
= 6^3x = 6^2
= 3x/3 = 2/3
A: x = 2/3
38. log4(1/32) = x
= 4x = 1/32
= 2^2x = 2^-5
= 2x/2 = -5/2
A: x = -5/2
40. log8(32) = x
= 8x = 32
= 2^3x = 2^5
= 3x/3 = 5/3
A: x = 5/3
C.
42. log4(64) - log3(81) - log(1/3)(81)
= log4(4^3) - log3(3^4) - log1/3(3^4)
= 3 - 4 - 4
A: -5
44. log1/9(27) - log8(32)/log81(1/64) - log10(100
A.
ReplyDelete2. log2n = -3
Answer: n = 1/8
4. log3(1/9) = n/3
= 3^(n/3) = 1/9
= n/3 = 1/9
= n/3 = -2/1
A: n = -6
6. log3(27) = 3n+6
= log3^3n+6 = 27
= 3n+6 = 3
= 3n/3 = -6+3/3
A: n = -1
8. log1/2n = -2
= 2^(-1)(-2) = n
A: n = 2
10. log8n = 1/3
12. log1/9(27) = n
= 1/9n = 27
= 3^-2n = 3^3
= -2n/-2 = 3/-2
A: n = -3/2
14. log9n = -1/2
= 9^-1/2 = n
= 3^(2)(-1/2) = n
= 3^-1 = n
A: n = -1
16. logx(9/4) = -2/3
= x^-2/3 = 9/4
= (-2/3) = (9/4) *cross multiply*
A: x = -1
20. logx(1/49) = -2
= x^-2 = 1/49
= -2 = -2
A: x = 1
B.
22. log3(1/9) = x
= 3x = 1/9
= 3x = 3^-2
A: x = -2
24. log10(0.01) = x
= 10x = 10^-3
A: x = -3
26. log4(2) = x
= 4x = 2
= 2^2x = 1
= 2x/2 = 1/2
A: x = 1/2
28. log3(27) = x
= 3x = 27
= 3x = 3^3
A: x = 3
30. log5(1) = x
= 5x = 1
A: x = 1
32. log1/4(2) = x
= 1/4x = 2
= 2^-2x = 2
= -2x/-2 = 1/-2
A: x = -1/2
34. log5(125) = x
= 5x = 125
= 5x = 5^3
A: x =3
36. log216(36) = x
= 216x = 36
= 6^3x = 6^2
= 3x/3 = 2/3
A: x = 2/3
38. log4(1/32) = x
= 4x = 1/32
= 2^2x = 2^-5
= 2x/2 = -5/2
A: x = -5/2
40. log8(32) = x
= 8x = 32
= 2^3x = 2^5
= 3x/3 = 5/3
A: x = 5/3
C.
42. log4(64) - log3(81) - log(1/3)(81)
= log4(4^3) - log3(3^4) - log1/3(3^4)
= 3 - 4 - 4
A: -5
44. log1/9(27) - log8(32)/log81(1/64) - log10(100)
gun min lee
ReplyDelete2. log base 2 of n=-3
2^-3=n
n=1/8
4. log base 3 of 1/9= n/3
3^n/3=1/9
3^n/3=3^-2
n/3=-2
n= -6
6. log base 3 of 27=3n+6
3^[3n+6]=27
3^[3n+6]=3^3
3n+6=3
3n=-3
n=-1
8. log base 1/2 of n= -2
1/2^-2= n
n=4
10. log base 8 of n=1/3
8^1/3=n
n=2
12. log base 1/9 of 27=n
1/9^n=27
3^-2n=3^3
-2n=3
n= -3/2
14. log base 9 of n= -1/2
9^-1/2=n
n=-3
16. log base x of 9/4=-2/3
x^-2/3=9/4
[x^-2/3=9/4]^-3/2
x=[9/4]^-3/2
x=3/2^-3
x=8/27
18. log base 3 of 1/27=n
3^n=1/27
3^n=3^-3
n= -3
20. log base x of 1/49=-2
x^-2=1/49
x^-2=7^-2
x=7
22. log base 3 of 1/9
3^n=1/9
3^n=3^-2
n= -2
24. log base 10 of .01
10^n=.01
n= -2
26. log base 4 of 2
4^n=2
2^2n=2^1
2n=1
n=1/2
28. log base 3 of 27
3^n=27
3^n=3^3
n=3
30. log base 5=1
5^n=1
n=0
32. log base 1/4 of 2
1/4^n=2
2^-2n=2
-2n=1
n= -1/2
34. log base 5 of 125
5^n=125
5^n=5^3
n=3
36. log base 216 of 36
216^n=36
6^3n=6^2
3n=2
n=2/3
38. log base 4 of 1/32
4^n=1/32
2^2n=2^-5
2n=-5
n= -5/2
40. log base 8 of 32
8^n=32
2^3n=2^5
3n=5
=n=5/3
42. [log base 4 of 64]-[log base 3 of 81]-[log base 1/3 of 81]
3-4-[-4]
=3
44.[log base 1/9 of 27-log base 8 of 32]/[log base 4 of 1/64-log base 10 of 100]
{[-3/2]-[5/3]}/{[-3]-[2]}
[-16/6]/-5
[-8/3]/-5
[-8/3][-1/5]
=8/15
Homework as of September 17, 2012
ReplyDeleteLogarithm
1.) Log2 n=-3
2^-3=n
n=1/8 •
2.) Log3 1/9=n/3
3^n/3=1/9
3^n/3=3^-2
(cube-root of)n/3=-2
N=-2 •
3.) Log3 27=3n + 6
3^3n+6=27
3^3n+6=3^3
3n+6=3
3n=3-6
N=-1 •
4.) Log1/2 n=-2
1/2^-2=n
N=4 •
5.) Log8 n=1/3
8 1/3=n
N=2 •
6.)Log1/9 27=n
1/9^n=27
3^-2n=3^3
-2n=3
N=-3/2 •
7.) Log9 n=-1/2
(square root of)9^-1/2=n
N=-3 •
8.) Log3 1/27=n
3^n=3^-3
N=-3 •
9.) Logx 1/49=-2
X^-2=7^-2
X=7 •
B.
1.) log3 1/9 = x
3^x=1/9
3^x=3^-2
X=-2 •
2.) log10 0.01=x
10^x=0.01
10^x=10^-2
X=-2 •
3.) log4 2=x
4^x=2
2^2x=2^1
X=1/2 •
4.) log3 27=x
3^x=27
3^x=3^3
X=3 •
5.) log5 1=x
5^x=1
X=0 •
6.) log1/4 2=x
1/4^x=2
2^-2x=2^1
-2x=1
X=-1/2 •
7.) log5 125=x
5^x=125
5^x=5^3
X=3 •
8.) log216 36=x
216^x=36
6^3x=6^2
3x=2
X=3/2 •
9.) log3 1/32=x
4^x=1/32
2^2x=2^-5
2x=-5
X=-5/2 •
10.) log8 32=x
8^x=32
2^3x=2^5
3x=5
X=5/3 •
C.
1.) log4 64 - log3 81 – log1/3 81
Log4 2^6 – log3 3^4 – log 1/3 3^4
6 – 4 – 4
-2 •
2.) log1/9 27 – log8 32
Log4 1/64 – log10 100
Log1/9 3^3 – log8 2^5
Log4 2^-6 – log10 10^2
3 – 5
-6 – 2
-1/4 •
Challenge:
1.) Logx (2x-3) = 1
X^1=2x – 3
X=2x-3
3=2x-x
X=3 •
Math HW p. 373-375
ReplyDeleteA.
2.) log2 n= -3
2^-3= n
n= 1/8
4.) log3 1/9 = n/3
3^n/3 = 1/9
3^n/3= -2/1
n= -6
6.) log3 27 = 3n+6
3^3n+6 = 27
3^3n+6= 3^3
3n=3-6
3n/3 = -3/3
n= -1
8.) log1/2 n = -2
1/2^-2= n
n= 4
10.) log8 n = 1/3
8^1/3 = n
n= 2
12.) log1/9 27 = n
1/9^n = 27
3^-2n = 3^3
-2n/-2= 3/-2
n= -3/2
14.) log9 n = -1/2
9^1/2 = n
n= 1/3
16.) logx9/4= -2/3
x^-2/3 = 9/4
-2/3 = 9/4
n= 3/2
18.) log3 1/27 = n
3^n = 1/27
3^n= 3^-3
n= -3
20.) logx 1/49 = -2
x^-2 = 1/49
x= 7
B.
22.) log3 1/9
3^x = 1/9
3^x = 3^-2
x= -2
24.) log10 0.01
10^x = 10^-2
x= -2
26.) log 4 2
4^x = 2
2^2x = 2^1
2x = 1
2x/2 = 1/2
x=1/2
28.) log3 27
3^x = 27
3^3 = 3^3
x= 3
30.) log5 1
5^x = 1
5^0x = 1
x= 0
32.) log1/4 2
1/4^x = 2
2^-2x = 2^1
-2x = 1
-2x/-2 = 1/-2
x= -1/2
34.) log5 125
5^x = 125
5^x = 5^3
x= 3
36.) log216 36
216^x = 36
6^3x = 6^2
3x = 2
3x/3 = 2/3
x= 2/3
38.) log4 1/32
4^x = 1/32
2^2x = 2^-5
2x = -5
2x/2 = -5/2
x= -5/2
40.) log8 32
8^x = 32
2^3x = 2^5
3x = 5
3x/3 = 5/3
x= 5/3
C.
42.) log4 64 - log3 81 - log1/3 81
= log4 4^3 - log3 3^4 - log1/3 1/3^-4
= 3 - 4 - (-4)
Final Answer= -3
44.) (log1/9 27 - log8 32)/(log4 64 - log10 100)
= (log1/9 1/9^-3/2 - log8 8^5/3)/(log4 4^-3 - log10 10^2)
= (-3/2 - 5/3)/(-3-2)
= (-19/6)/(-5/1)
Final Answer= -19/30
Jeremy D. Pascua
ReplyDeletepp. 373-375
Written Math
Letter A
2.) n= 1/8
4.) n= -6
6.) n= -1
8.) n= 4
10.) n= 2
12.) n= -3/2
14.) n= 1/3
16.) x= (blank)
18.) n= (blank)
20.) n= 7
Letter B
22.) x= -2
24.) x= -2
26.) x= 1/2
28.) x= 3
30.) x= 1
32.) x= -1/2
34.) x= 3
36.) x= 2/3
38.) x= -5/2
40.) x= 5/3
Bk. Page 373
ReplyDeleteA.
2. ) 2^-3=n
-8=n
4.) 3^n/3=1/9
3^n/3=3^-2
n/3=-2
n=-6
6.) 3^3n+6=3^2
3n+6=2
3n=-4
n= -4/3
8.) ½^-2 = n
2^(-1)(-2)=n
-3=n
10.) 8^1/3=n
∛8 = n
2=n
12.) 1/9^n=27
3^-2n=3^3
-2n=3
n=-3/2
14.) 9^1/2=n
√9 =n
3=n
16.) 3/2^( x^2/3=9/4 ) ^3/2
x=9/4^-3/2
x=0.3
18.) 3^n=1/27
3^n=3^-3
n=-3
20.) x^-2=1/49
x^-2=7^-2
x=7
B.
22.) 3^x =1/9
3^x=3^-2
x=-2
24.) 10^x = 1/100
10^x=10^-2
x=-2
26.) 4^x=2
2^2x=2
2x=2
x=1
28.) 3^x=27
3^x=3^3
x=3
30.) 5^x=1
5^x=5^0
x=0
32.) 1/4^x=2
2^-2x=2
x=-1
34.) 5^x=125
5^x=5^3
x=3
36.) 216^x=36
6^3x=6^2
x=2/3
38.) 4^x=1/32
2^2x=2^-5
x=-5/2
40.) 8^x=3^2
2^3x=2^5
x=5/3
42.) 4^x=64 3^x=81 1/3^x=81
x= 3 x= 4 x=-4
3-4-(-4)
x=3
44.) 3^-2x=3^3 2^3x=2^5 / 4^x=4^3 10^x=10^2
x= -3/2 x= 5/3 x=-3 x=2
(-3/2 - 5/3) / (-3-2)
LCD: (-9/6 - 10/6) / -5
-19/6 / -5
x=19/30
HOMEWORK 09/17/2012
ReplyDeletelog2 n = -3
2^-3 = n
--> n = 1/8
log3 1/9 =n/3
3^n/3 = 1/9
3^n/3 = 3^-2
n/3 = -2
[n/3 = -2]3
--> n = -6
log3 27 = 3n + 6
3^3n+6 = 27
3^3n+6 = 3^3
3n+6 = 3
3n = 3-6
[3n = 3-6]/3
n = 3-6/3
n = -3/3
--> n= -1
log1/2 n = -2
1/2^-2 = n
--> n = 4
log8 n = 1/3
8^1/3 = n
--> n = 1.9 or 19/10
log1/9 27 = n
1/9^n = 27
3^-2n = 3^3
-2n = 3
[-2n = 3]/-2
--> n = -3/2
log9 n= -1/2
9^-1/2 = n
--> n = 1/3
logx 9/4 = -2/3
x^-2/3 = 9/4
[x^-2/3 = 9/4]^-3/2
x = 9/4^-3/2
--> x = 0.3
log3 1/27 = n
3^n = 1/27
--> n = -3
logx 1/49 = -2
x^-2 = 1/49
--> x = 7
log3 1/9
log3 1/9 = x
3^x = 1/9
--> x = -3
log10 0.01
log10 0.01 = x
10^x = 0.01
10^x = 10^-2
--> x = -2
log3 27
log3 27 = x
3^x = 27
3^x = 3^3
--> x = 3
log5 1
log 5 1 = x
5^x = 1
--> x = 0
log1/4 2
log1/4 2 = x
1/4^x = 2
2^-2x = 2^1
-2x = 1
[-2x = 1]/-2
--> x= -1/2
log5 125
log5 125 = x
5^x = 125
5^x = 5^3
--> x = 3
log216 36
log 216 36 = x
216^x = 36
6^3x = 6^2
3x = 2
[3x = 2]/3
--> x = 2/3
log4 1/32
log 4 1/32 = x
4^x = 1/32
2^2x = 2^-5
2x = -5
[2x = -5]/2
--> x = -5/2
log8 32
log8 32 = x
8^x = 32
2^3x = 2^5
3x = 5
[3x = 5]/3
--> x = 5/3
log4 64 - log3 81 - log1/3 81
log4 64
log4 64 = x
4^x = 64
x = 3
log3 81
log3 81 = x
3^x = 81
x = 4
log1/3 81
log1/3 81 = x
1/3^x = 81
x = -4
3 - 4 - (-4)
= 3 <--
log1/9 27 - log8 32/ log4 1/64 - log10 100
log1/9 27
log1/9 27 = x
1/9^x = 27
3^-2x = 3^3
-2x = 3
[-2x = 3]/-2
x = -3/2
log8 32
log8 32 = x
8^x = 32
2^3x = 2^5
3x = 5
[3x = 5]/3
x = 5/3
log4 1/64
log4 1/64 = x
4^x = 1/64
x = -3
log10 100
log10 100 = x
10^x = 100
x = 2
-3/2 - 5/3/ -3 - 2
-9/6 - 10/6/ -5
-19/6/-5
= 19/30 <---
11. log3 4x^2 y^5
ReplyDelete►log3 4 + 2log3 x + 5log3 y
12. log5 3y/ 4th root [2x]
►log5 3 + log5 y - 1/4log5 2 + 1/4log5 x
13. log6 cuberoot[2y/x^2]
►1/3log6 2 + 1/3 log6 y - 2/3 log6 x
14. logx 5a^3 b^2 c^4
►logx 5 + 3logx a + 2logx b + 4logx c
15. logx cuberoot[a^2 b^2]/ sqreroot c
►2/3logx a + 2/3logx b - 1/2logx c
16. loga x^3/5y
►3loga x - loga 5 + loga y
17. log10 sqreroot[2x/y]
►1/2log10 2 + 1/2log10 x - 1/2log10 y
18. log3 sqreroot[ac^2]/b
►1/2log3 a + log3 c - log3 b
19. log2 4throot[a^3 b^2 c]/2
►3/4log2 a + 1/2log2 b + 1/4log2 c - log2 2
20. log5 [8x]^2/4th root [y^3]
►2log5 8 + 2log5 x - 3/4log5 y
Assignment
ReplyDeletepage 389 nos. 11-20
11 log base 3 of 4*x^2*y^5
log base 3 of 4 + log base 3 of x^2 + log base 3 of y^5
►log base 3 of 4 + 2 log base 3 of x + 5 log base 3 of y*
12 log base 5 of 3y/4√2x
log base 5 of 3 + log base 5 of y - log base 5 of 4√2 + log base 5 of 4√x
log base 5 of 3 + log base 5 of y - log base 5 of [4√2]^1/4 + log base 5 of [4√x]^1/4
log base 5 of 3 + log base 5 of y - log base 5 of 2^1/4 + log base 5 of x^1/4
►log base 5 of 3 + log base 5 of y - 1/4 log base 5 of 2 + 1/4 log base 5 of x*
13 log base 6 of 3√2y/x^2
log base 6 of 3√2y - log base 6 of 3√x^2
log base 6 of 3√2 + log base 6 3√y - log base 6 of 3√x^2
log base 6 of [3√2]^1/3 + log base 6 [3√y]^1/3 - log base 6 of [3√x^2]^1/3
log base 6 of 2^1/3 + log base 6 y^1/3 - log base 6 of (x^2)^1/3
1/3 log base 6 of 2 + 1/3 log base 6 y - 1/3 log base 6 of x^2
1/3 log base 6 of 2 + 1/3 log base 6 y - 1/3*2 log base 6 of x
►1/3 log base 6 of 2 + 1/3 log base 6 y - 2/3 log base 6 of x*
14 log base x of 5*a^3*b^2*c^4
log base x of 5 + log base x of a^3 + log base x of b^2 + log base x of c^4
►log base x of 5 + 3 log base x of a + 2 log base x of b + 4 log base x of c*
15 log base x of 3√a^2*b^2/√c
log base x of 3√a^2 + log base x of 3√b^2 - log base x of √c
log base x of [3√a^2]^1/3 + log base x of [3√b^2]^1/3 - log base x of [√c]^1/2
log base x of (a^2)^13 + log base x of (b^2)^1/3 - log base x of c^1/2
1/3 log base x of a^2 + 1/3 log base x of b^2 - 1/2 log base x of c
1/3*2 log base x of a + 1/3*2 log base x of b - 1/2 log base x of c
►2/3 log base x of a + 2/3 log base x of b - 1/2 log base x of c*
16 log base a of x^3/5y
log base a of x^3 - log base a of 5 + log base a of y
►3 log base a of x - log base a of 5 + log base a of y*
17 log base 10 of √2x/y
log base 10 of √2x - log base 10 of √y
log base 10 of √2 + log base 10 of √x - log base 10 of √y
log base 10 of [√2]^1/2 + log base 10 of [√x]^1/2 - log base 10 of [√y]^1/2
log base 10 of 2^1/2 + log base 10 of x^1/2 - log base 10 of y^1/2
►1/2 log base 10 of 2 + 1/2 log base 10 of x - 1/2 log base 10 of y*
18 log base 3 of √ac^2 /b
log base 3 of √ac^2 - log base 3 of b
log base 3 of √a + log base 3 of √c^2 - log base 3 of b
log base 3 of [√a]^1/2 + log base 3 of [√c^2]^1/2 - log base 3 of b
log base 3 of a ^1/2 + log base 3 of (c^2)^1/2 - log base 3 of b
1/2 log base 3 of a + 1/2 log base 3 of c^2 - log base 3 of b
1/2 log base 3 of a + 1/2*2 log base 3 of c - log base 3 of b
1/2 log base 3 of a + 2/2 log base 3 of c - log base 3 of b
►1/2 log base 3 of a + log base 3 of c - log base 3 of b*
19 log base 2 of 4√a^3*b^2*c /2
log base 2 of 4√a^3*b^2*c - log base 2 of 2
log base 2 of 4√a^3 + log base 2 of 4√b^2 + log base 2 of 4√c - log base 2 of 2
log base 2 of [4√a^3]^1/4 + log base 2 of [4√b^2]^1/4 + log base 2 of [4√c]^1/4 - log base 2 of 2
log base 2 of (a^3)^1/4 + log base 2 of (b^2)^1/4 + log base 2 of c^1/4 - log base 2 of 2
log base 2 of 1/4 a^3 + log base 2 of 1/4 b^2+ 1/4 log base 2 of c - log base 2 of 2
1/4*3 log base 2 of a + 1/4*2 log base 2 of b + 1/4 log base 2 of c - log base 2 of 2
3/4 log base 2 of a + 2/4 log base 2 of 2/4 b + 1/4 log base 2 of c - log base 2 of 2
►3/4 log base 2 of a + log base 2 of 1/2 b + 1/4 log base 2 of c - log base 2 of 2*
20 log base 5 of (8x)^2 / 4√y^3
log base 5 of 8^2 + log base 5 of x^2 - log base 5 of 4√y^3
2 log base 5 of 8 + 2 log base 5 of x - log base 5 of [4√y^3]^1/4
2 log base 5 of 8 + 2 log base 5 of x - log base 5 of (y^3)^1/4
2 log base 5 of 8 + 2 log base 5 of x - 1/4 log base 5 of y^3
2 log base 5 of 8 + 2 log base 5 of x - 1/4*3 log base 5 of y
►2 log base 5 of 8 + 2 log base 5 of x - 3/4 log base 5 of y*
Homework p. 389 B
ReplyDeleteSolutions:
#11 log3 4x^2y^5
log3 4 + log3 x^2 + log3 y^5
log3 4 + 2log3 x + 5log3 y ✓
#12 log5 3y/∜2x
log5 3 + log5 y - 1/4 log5 2 - 1/4 log5 x ✓
#13 log6 ∛2y/x^2
1/3 log6 2 + 1/3 log6 y - 1/3 log6 x^2
1/3 log6 2 + 1/3 log6 y - 2/3 log6 x ✓
#14 logx 5a^3b^2c^4
logx 5 + logx a^3 + logx b^2 + logx c^4
logx 5 + 3 logx a + 2 logx b + 4 logx c ✓
#15 logx ∛a^2b^2/√c
1/3 logx a^2 + 1/3 logx b^2 / 1/2 logx c
2/3 logx a + 2/3 logx b / 1/2 logx c ✓
#16 loga x^3/5y
loga x^3 - loga 5 + loga y
3 loga x - loga 5 + loga y ✓
#17 log10 √2x/y
1/2 log10 2 + 1/2 log10 x - 1/2 log10 y ✓
#18 log3 √ac^2/b
1/2 log3 a + 1/2 log3 c^2 - log3 b
1/2 log3 a + log3 c - log3 b ✓
#19 log2 ∜a^3b^2c/2
1/4 log2 a^3 + 1/4 log2 b^2 + 1/4 log2 c - log2 2
3/4 log2 a + 1/2 log2 b + 1/4 log2 c - log2 2 ✓
#20 log5 (8x)^2/∜y3
log5 8^2 + log5 x^2 - 1/4 log5 y^3
2log5 8 + 2 log5 x - 3/4 log5 y ✓
Math Homework for September 18, 2012
ReplyDeletep. 389; Letter B
11) log3 4x^2y^5
ANSWER: log3 4 + 2log3 x + 5log3 y
12) log5 (3y)/fourth root of 2x
ANSWER: log5 3 + log5 y - 1/4log5 2 + 1/4log5 x
13) log6 cube root of (2y)/x^2
ANSWER: 1/3log6 2 + 1/3log6 y - 2/3 log6 x
14) logx 5a^3b^2c^4
ANSWER: logx 5 + 3logx a + 2logx b + 4logx c
15) logx (cube root of a^2b^2)/square root of c
ANSWER: 2/3logx a + 2/3logx b - 1/2logx c
16) loga (x^3)/5y
ANSWER: 3loga x - loga 5 + loga y
17) log10 square root of (2x)/y
ANSWER: 1/10log10 2 + 1/10log x - 1/10log10 y
18) log3 (square root of ac^2)/b
ANSWER: 1/2log3 a + log3 c - log3 b
19) log2 (fourth root of a^3b^2c)/2
ANSWER: 3/4log2 a + 1/2log2 b + 1/4log2 c - log2 2
20) log5 [(8x)^2]/fourth root of y^3
ANSWER: 2log5 * + 2log5 x - 3/4log5 y
Fristine
ReplyDeleteHW
11.) log base 3 of 4*x^2*y^5
log base 3 of 4 + log base 3 of x^2 + log base 3 of y^5
log base 3 of 4 + 2 log base 3 of x + 5 log base 3 of y*
12.) log base 5 of 3y/4√2x
log base 5 of 3 + log base 5 of y - log base 5 of 4√2 + log base 5 of 4√x
log base 5 of 3 + log base 5 of y - log base 5 of [4√2]^1/4 + log base 5 of [4√x]^1/4
log base 5 of 3 + log base 5 of y - log base 5 of 2^1/4 + log base 5 of x^1/4
log base 5 of 3 + log base 5 of y - 1/4 log base 5 of 2 + 1/4 log base 5 of x*
13.) log base 6 of 3√2y/x^2
log base 6 of 3√2y - log base 6 of 3√x^2
log base 6 of 3√2 + log base 6 3√y - log base 6 of 3√x^2
log base 6 of [3√2]^1/3 + log base 6 [3√y]^1/3 - log base 6 of [3√x^2]^1/3
log base 6 of 2^1/3 + log base 6 y^1/3 - log base 6 of (x^2)^1/3
1/3 log base 6 of 2 + 1/3 log base 6 y - 1/3 log base 6 of x^2
1/3 log base 6 of 2 + 1/3 log base 6 y - 1/3*2 log base 6 of x
1/3 log base 6 of 2 + 1/3 log base 6 y - 2/3 log base 6 of x*
14.) log base x of 5*a^3*b^2*c^4
log base x of 5 + log base x of a^3 + log base x of b^2 + log base x of c^4
log base x of 5 + 3 log base x of a + 2 log base x of b + 4 log base x of c*
15.) log base x of 3√a^2*b^2/√c
log base x of 3√a^2 + log base x of 3√b^2 - log base x of √c
log base x of [3√a^2]^1/3 + log base x of [3√b^2]^1/3 - log base x of [√c]^1/2
log base x of (a^2)^13 + log base x of (b^2)^1/3 - log base x of c^1/2
1/3 log base x of a^2 + 1/3 log base x of b^2 - 1/2 log base x of c
1/3*2 log base x of a + 1/3*2 log base x of b - 1/2 log base x of c
2/3 log base x of a + 2/3 log base x of b - 1/2 log base x of c*
16.) log base a of x^3/5y
log base a of x^3 - log base a of 5 + log base a of y
3 log base a of x - log base a of 5 + log base a of y*
17.) log base 10 of √2x/y
log base 10 of √2x - log base 10 of √y
log base 10 of √2 + log base 10 of √x - log base 10 of √y
log base 10 of [√2]^1/2 + log base 10 of [√x]^1/2 - log base 10 of [√y]^1/2
log base 10 of 2^1/2 + log base 10 of x^1/2 - log base 10 of y^1/2
1/2 log base 10 of 2 + 1/2 log base 10 of x - 1/2 log base 10 of y*
18.) log base 3 of √ac^2 /b
log base 3 of √ac^2 - log base 3 of b
log base 3 of √a + log base 3 of √c^2 - log base 3 of b
log base 3 of [√a]^1/2 + log base 3 of [√c^2]^1/2 - log base 3 of b
log base 3 of a ^1/2 + log base 3 of (c^2)^1/2 - log base 3 of b
1/2 log base 3 of a + 1/2 log base 3 of c^2 - log base 3 of b
1/2 log base 3 of a + 1/2*2 log base 3 of c - log base 3 of b
1/2 log base 3 of a + 2/2 log base 3 of c - log base 3 of b
1/2 log base 3 of a + log base 3 of c - log base 3 of b*
19.) log base 2 of 4√a^3*b^2*c /2
log base 2 of 4√a^3*b^2*c - log base 2 of 2
log base 2 of 4√a^3 + log base 2 of 4√b^2 + log base 2 of 4√c - log base 2 of 2
log base 2 of [4√a^3]^1/4 + log base 2 of [4√b^2]^1/4 + log base 2 of [4√c]^1/4 - log base 2 of 2
log base 2 of (a^3)^1/4 + log base 2 of (b^2)^1/4 + log base 2 of c^1/4 - log base 2 of 2
log base 2 of 1/4 a^3 + log base 2 of 1/4 b^2+ 1/4 log base 2 of c - log base 2 of 2
1/4*3 log base 2 of a + 1/4*2 log base 2 of b + 1/4 log base 2 of c - log base 2 of 2
3/4 log base 2 of a + 2/4 log base 2 of 2/4 b + 1/4 log base 2 of c - log base 2 of 2
3/4 log base 2 of a + log base 2 of 1/2 b + 1/4 log base 2 of c - log base 2 of 2*
20.) log base 5 of (8x)^2 / 4√y^3
log base 5 of 8^2 + log base 5 of x^2 - log base 5 of 4√y^3
2 log base 5 of 8 + 2 log base 5 of x - log base 5 of [4√y^3]^1/4
2 log base 5 of 8 + 2 log base 5 of x - log base 5 of (y^3)^1/4
2 log base 5 of 8 + 2 log base 5 of x - 1/4 log base 5 of y^3
2 log base 5 of 8 + 2 log base 5 of x - 1/4*3 log base 5 of y
2 log base 5 of 8 + 2 log base 5 of x - 3/4 log base 5 of y
#11
ReplyDeletelog base 3^(4x^2)(y^5)
=log base 3^4 + 2log base 3^x + 5log base 3^y
#12
log base 5^3y/fourth root of 2x
=log base 5^3 + log base 5^y - 1/4log base 5^2 +1/4log base 5^x
#13
log base 6 cube root of 2y/ cube root of x^2
=1/3log base 6^2 + 1/3log base 6^y
#14
log base x^5(a^3)(b^2)(c^4)
=log base x ^5 + 3log base x^a + 2log base x^b + 4log base x^c
#15
log base x^ cube root of (a^2)(b^2)/square root of c
=2/3log base x^a +2/3log base x^b - 1/2log base x^c
#16
log base a^(x^3)/5y
=3log base a^x - log base a^5 + log base a^y
#17
log base 10^square root of 2x/the squarre root of y
=1/2log base 10^2 + 1/2log base 10^x - 1/2log base 10^y
#18
log base 3^ square root of (9c^3)/b
=1/2log base 3^9 + log base 3^c - log base 2^2
#19
log base 2^ the fourth root of (a^3)(b^2)(c)/2
=3/4log base 2^9 + 1/2log base 2^b + 1/4log base x^c - log base 2^2
#20
log base 5^(8x^2)/fourth root of y^3
=log base 5^64 + 2log base 5^x - 3/4log base 5^y
#11 log3 4x^2 y^5
ReplyDelete=log3 4 + 2log3 x + 5log3 y
#12 log5 3y/ 4th√2x
=log5 3 + log5 y - 1/4log5 2 + 1/4log5 x
#13 log6 cube√2y/x^2
=1/3log6 2 + 1/3 log6 y - 2/3 log6 x
#14 logx 5a^3 b^2 c^4
=logx 5 + 3logx a + 2logx b + 4logx c
#15 logx cube√a^2 b^2/ √c
=2/3logx a + 2/3logx b - 1/2logx c
#16 loga x^3/5y
=3loga x - loga 5 + loga y
#17 log10 √2x/y
=1/2log10 2 + 1/2log10 x - 1/2log10 y
#18 log3 √ac^2/b
=1/2log3 a - log3 b + log3 c
#19 log2 4th√a^3 b^2 c/2
=3/4log2 a + 1/2log2 b + 1/4log2 c - log2 2
#20 log5 8x^2/4th√y^3
=2log5 8 + 2log5 x - 3/4log5 y
9/18/12
-Nathan Fuster-
Homework
ReplyDeleteSeptember 18 2012
11. log3 4x^2 y^5
log base 3 of 4 + log base 3 of x^2 + log base 3 of y^5
------log base 3 of 4 + 2 log base 3 of x + 5 log base 3 of y*
12. log base 5 of 3y/4√2x
log base 5 of 3 + log base 5 of y - log base 5 of 4√2 + log base 5 of 4√x
log base 5 of 3 + log base 5 of y - log base 5 of [4√2]^1/4 + log base 5 of [4√x]^1/4
log base 5 of 3 + log base 5 of y - log base 5 of 2^1/4 + log base 5 of x^1/4
---------log base 5 of 3 + log base 5 of y - 1/4 log base 5 of 2 + 1/4 log base 5 of x*
13. log base 6 of 3√2y/x^2
log base 6 of 3√2y - log base 6 of 3√x^2
1/3 log base 6 of 2 + 1/3 log base 6 y - 1/3*2 log base 6 of x
-------1/3 log base 6 of 2 + 1/3 log base 6 y - 2/3 log base 6 of x*
14. logx 5a^3 b^2 c^4
log base x of 5 + log base x of a^3 + log base x of b^2 + log base x of c^4
-----log base x of 5 + 3 log base x of a + 2 log base x of b + 4 log base x of c*
15. log base x of 3√a^2*b^2/√c
log base x of 3√a^2 + log base x of 3√b^2 - log base x of √c
1/3 log base x of a^2 + 1/3 log base x of b^2 - 1/2 log base x of c
1/3*2 log base x of a + 1/3*2 log base x of b - 1/2 log base x of c
-------2/3 log base x of a + 2/3 log base x of b - 1/2 log base x of c*
16. loga x^3/5y
log base a of x^3 - log base a of 5 + log base a of y
-----3 log base a of x - log base a of 5 + log base a of y*
17. log base 10 of √2x/y
log base 10 of √2x - log base 10 of √y
log base 10 of √2 + log base 10 of √x - log base 10 of √y
log base 10 of [√2]^1/2 + log base 10 of [√x]^1/2 - log base 10 of [√y]^1/2
log base 10 of 2^1/2 + log base 10 of x^1/2 - log base 10 of y^1/2
-----1/2 log base 10 of 2 + 1/2 log base 10 of x - 1/2 log base 10 of y*
18. log base 3 of √ac^2 /b
log base 3 of √ac^2 - log base 3 of b
log base 3 of √a + log base 3 of √c^2 - log base 3 of b
1/2 log base 3 of a + 1/2*2 log base 3 of c - log base 3 of b
1/2 log base 3 of a + 2/2 log base 3 of c - log base 3 of b
-------1/2 log base 3 of a + log base 3 of c - log base 3 of b*
19. log base 2 of 4√a^3*b^2*c /2
log base 2 of 4√a^3*b^2*c - log base 2 of 2
log base 2 of 4√a^3 + log base 2 of 4√b^2 + log base 2 of 4√c - log base 2 of 2
1/4*3 log base 2 of a + 1/4*2 log base 2 of b + 1/4 log base 2 of c - log base 2 of 2
3/4 log base 2 of a + 2/4 log base 2 of 2/4 b + 1/4 log base 2 of c - log base 2 of 2
-----3/4 log base 2 of a + log base 2 of 1/2 b + 1/4 log base 2 of c - log base 2 of 2*
20. log base 5 of (8x)^2 / 4√y^3
log base 5 of 8^2 + log base 5 of x^2 - log base 5 of 4√y^3
2 log base 5 of 8 + 2 log base 5 of x - 1/4 log base 5 of y^3
2 log base 5 of 8 + 2 log base 5 of x - 1/4*3 log base 5 of y
------2 log base 5 of 8 + 2 log base 5 of x - 3/4 log base 5 of y
HOMEWORK AS OF September 18, 2012
ReplyDelete1.) Log3 4x^2y^5
2log3 4 + 2log3 x + 5log3 y
2.) Log5 3y/fourth-root of 2x^2
Log5 3 + log5 y – 1/4log5 2 + 1/4log5 X
3.) Log6 cube-root of 2y/x^2
1/3log6 2 + 1/3log6 y – 2/3log6 X
4.) Logx 5^3b^2c^4
3logx 5 + 3logx a + 2logx b + 4logx c
5.) Logx cube-root of a^2b^2
2/3logx a + 2/3logx b – 1/2logx c
6.) Loga x^3/5y
3loga x – loga 5 + loga y
7.) Log10 square-root of 2x/y
1/2log10 2 + 1/2log10 x – 1/2log10 y
8.) Log3 square-root of ac^2 OVER b
1/2log3 a + 1/2log3 c – log3 b
9.) Log2 fourth-root of a^3b^2c OVER 2
3/4log2 a + 2/4log2 b + 1/4log2 c – log2 2
10.) Log5 (8x)^2/fourth-root of y^3
1/2log5 8 + 1/2log5 x – 3/4log5 y
Math HW
ReplyDeletep. 389 B, 11-20
11. log 3 4x^ 2y^5
= log3 4 + 2log3 x + 5log3 y
12. log 5 3y/42x
= log5 3 + log5 y – log5 42x
= log5 3 + log5 y- ¼ log5 2 + ¼ log5x
13. log 6 32y/x^2
= 1/3log6 2 + 1/3log6 y – 2/3log6 x
14. logx 5a^3b^2c^4
= logx 5 + 3logx a + 2logx b + 4logx c
15. logx 3a^2b^2/c
=2/3logx a + 2/3logx b - ½ logx c
16. loga x^3/5y
= 3loga x – loga 5 + loga y
17. log10 √2x/y
= ½ log10 2 + ½ log10 x – 1/2log10 y
18. log3 ac^2/b
= ½ log3 a + log3 c – log3 b
19. log2 4a^3b^2c/2
= ¾log2 a + ½ log2 b + ¼ log2 c - log2 2
20. log5(8x)^2/4y3
= 2log5 8 + 2log5 x – 3/4log 5 y
hw math p 389
ReplyDelete11). log3 4x^2 y^5
fa= log3 4 + 2log3 x + 5log3 y
12). log5 3y/ [4th rt 2x]
fa= log5 3 + log5 y - 1/4log5 2 + 1/4log5 x
13). log6 crt [2y/x^2]
fa= 1/3log6 2 + 1/3 log6 y - 2/3 log6 x
14). logx [5a^3 b^2 c^4]
fa= logx 5 + 3logx a + 2logx b + 4logx c
15). logx cuberoot[a^2 b^2]/ src c
fa= 2/3logx a + 2/3logx b - 1/2logx c
16). loga x^3/5y
fa= 3loga x - loga 5 + loga y
17). log10 sqreroot[2x/y]
fa= 1/2log10 2 + 1/2log10 x - 1/2log10 y
18). log3 sqreroot[ac^2]/b
fa= 1/2log3 a + log3 c - log3 b
19). log2 4throot[a^3 b^2 c]/2
fa= 3/4log2 a + 1/2log2 b + 1/4log2 c - log2 2
20). log5 [8x]^2/4th root [y^3]
fa= 2log5 8 + 2log5 x - 3/4log5 y
HOMEWORK 9/18/12
ReplyDeletepp 389 11-20
11. log3 4x^2y^5
= log3 4 + 2log3 x + 5log3 y
12. log5 3y/^4 square root(2x)
= log5 3 + log5 y - log5 1/4 2 + log5 1/4 x
13. log6 3 square root 2y/x^2
= log1/3 + log6 1/3 - log6 2/3 x
14. logx 5a^3b^2c^4
= logx 5 + 3logx a + 2logx b + 4logx c
15. logx sqaureroot 3(a^3b^2)/squareroot (c)
= log3 a + 1/3log3 b + log3 2
16. loga x^3/5y
= logx 3loga + loga 5 + loga y
17. log10 squareroot 2x/y
= log10 2 1/10 + log10 x + log10 y
18. log3 squareroot ac^2/b
= 1/2log3 a + log3 c + log3 b
19. log2 squareroot 4a^3b^2c/2
= 1/3log2 a + 1/2log2 b + log2 c
20. log5 (8x)^2 sqaureroot 4(y^3)
= 2log5 x + 2log5 y + 3/4log 5
11. log3 4x^2 y^5
ReplyDeleteA: log3 4 + 2log3 x + 5log3 y
12. log5 3y/ '4th root' [2x]
A: log5 3 + log5 y - 1/4log5 2 + 1/4log5 x
13. log6 'cuberoot'[2y/x^2]
A: 1/3log6 2 + 1/3 log6 y - 2/3 log6 x
14. logx 5a^3 b^2 c^4
A: logx 5 + 3logx a + 2logx b + 4logx c
15. logx 'cuberoot'[a^2 b^2]/ sqreroot c
A: 2/3logx a + 2/3logx b - 1/2logx c
16. loga x^3/5y
A: 3loga x - loga 5 + loga y
17. log10 'sqreroot'[2x/y]
A: 1/2log10 2 + 1/2log10 x - 1/2log10 y
18. log3 sqreroot[ac^2]/b
A: 1/2log3 a + log3 c - log3 b
19. log2 '4throot'[a^3 b^2 c]/2
A: 3/4log2 a + 1/2log2 b + 1/4log2 c - log2 2
20. log5 [8x]^2/'4th root' [y^3]
A: 2log5 8 + 2log5 x - 3/4log5 y
assignment September 18,2012
ReplyDelete11. log3 4x^2 y^5
F.A- log3 4+ 2log3 x+ 5log3 y
12.log5 3y/4squared 2x
F.A- log5 3 + log5 y - 1/4log5 2 - 1/4log5 x
13.log6 3squareroot of 2y divide by x^2
F.A- 1/3log6 2+ 1/3log6 y- 2/3log6 x
14.logx 5a^3b^2c^4
F.A- logx 5+ 3logx a+ 2logx b+ 4logx c
15.logx 3squareroot of a^2 b^2 divide by square root of C
F.A- 2/3logx a+ 2/3logx b+ 1/2logx c
16.logb x^3 divide by 5y
F.A- 3loga x- loga 5+ loga y
17.log10 square root of 2x divide by y
F.A- 1/2log10 2+ 1/2log10 x- 1/2log10 y
18.log3 square root of ac^2 divide by b
F.A- 1/2log3 a+ log3 c- log3 b
19.log2 4square root of a^3 B^2 c divide by 2
F.A- 3/4log2 a+ 1/2log2 b+ 1/4log2 c-log2 2
20.log5 8x1^2 divide by 4square root of x^3
F.A- 2log5 x+ 2log5 x- 3/4log5 y
-carlos diego domagas
Sept 18,2012
ReplyDeleteHomework
p. 389
11.) log3 4x^2 y^5
-> log3 4 + 2log3 x + 5log3 y
12.) log5 3y/fourth root of 2x
-> log5 3 + log5 y - 1/4log5 2 + 1/4log5 x
13.) log6 cube root of 2y/x^2
-> 1/3log6 2 + 1/3log6 y - 1/3 log6 x + 2/3log6 x
14.) logx 5a^3 b^2 c^4
-> logx 5 + 3logx a + 2logx b + 4logx c
15.) logx cube root of a^2 b^2 /square root of c
-> 2/3logx a + 2/3logx b - 1/2logx c
16.) loga x^3/5y
-> 3loga x - loga 5 + loga y
17.) log10 square root of 2x / y
-> 1/10log10 2 + 1/10log x - 1/10log10 y
18.) log3 square root of ac^2 / b
-> 1/2log3 a + log3 c - log3 b
19) log2 fourth root of a^3 b^2c / 2
-> 3/4log2 a + 1/2log2 b + 1/4log2 c + log2 2
20) log5(8x)^2 / fourth root of y^3
-> 2log5 8 + 2log5 x - 3/4log5 y
MIKA LAPUS
ReplyDeleteHomework 09/19/12
page 389, Letter B
11.) log3 4x^2y^5
= log3 4 + 2log3 x + 5log3 y ♦
12.) log5 3y/(fourth root of 2x)
= log5 3 + log5 y - 1/4log5 2 + 1/4log5 x ♦
13.) log6 (cube root of 2y/x^2)
=1/3log6 2 + 1/3log6 y - 2/3 log6 x ♦
14.) logx 5a^3b^2c^4
= logx 5 + 3logx a + 2logx b + 4logx c ♦
15.) logx (cube root of a^2b^2)/square root of c
= 2/3logx a + 2/3logx b - 1/2logx c ♦
16.) loga (x^3)/5y
= 3loga x - loga 5 + loga y ♦
17.) log10 (square root of (2x)/y)
= 1/10log10 2 + 1/10log x - 1/10log10 y ♦
18.) log3 (square root of ac^2)/b
= 1/2log3 a + log3 c - log3 b ♦
19.) log2 (fourth root of a^3b^2c)/2
=3/4log2 a + 1/2log2 b + 1/4log2 c - log2 2 ♦
20.) log5 [(8x)^2]/(fourth root of y^3)
= 2log5 * + 2log5 x - 3/4log5 y ♦
Homework for September 18, 2012
ReplyDeleteB.
#11. log3 4x^2y^5
[log3 4 + 2log3 x + 5log3 y]
#12. log5 3y/4throot{2x}
[log5 3 + log5 y - 1/4log5 2 + 1/4log5 x]
#13. log6 cuberoot{2y/x^2}
[1/3log6 2 + 1/3log6 y - 1/3log6 x^2]
#14. logx 5a^3b^2c^4
[logx 5 + 3logx a + 2logx b + 4logx c]
#15. logx cuberoot{a^2b^2}/squareroot{c}
[2/3logx a + 2/3logx b - 1/2logx c]
#16. loga x^3/5y
[3loga x - loga 5 + loga y]
#17. log10 squareroot{2x/y}
[1/2log10 2 + 1/2log10 x - 1/2log10 y]
#18. log3 squareroot{ac^2}/b
[1/2 log3 a + log3 2 - log3 b]
#19. log2 fourthroot{a^3b^2c}/2
[3/4log2 a + 1/2log2 b + 1/4log2 c - log2 2]
#20. log5 (8x)^2/fourthroot{y^3}
[log5 64 + 2log5 x - 3/4 log5 y]
Homework in math
ReplyDelete11) log3 4x^2y^5
= log3 4 + 2log3 x + 5log3 y
12) log5 3y/∜2x
= log5 3 + log5 y - 1/4log5 2 + 1/4log5 x
13) log6 ∛2y/x^2
= 1/3log6 2 + 1/3log6 y - 2/3 log6 x
14) logx 5a^3b^2c^4
= logx 5 + 3logx a + 2logx b + 4logx c
15) logx ∛a^2b^2/√c
= 2/3logx a + 2/3logx b - 1/2logx c
16) loga (x^3)/5y
= 3loga x - loga 5 + loga y
17) log10 √2x/y
= 1/10log10 2 + 1/10log x - 1/10log10 y
18) log3 √ac^2/b
= 1/2log3 a + log3 c - log3 b
19) log2 ∜a^3b^2c/2
= 3/4log2 a + 1/2log2 b + 1/4log2 c - log2 2
20) log5 (8x)^2/∜y3
= 2log5 * + 2log5 x - 3/4log5 y
HOMEWORK 09/18/2012
ReplyDeletelog3 4x^2y^5
ANSWER: log3 4 + 2log3 x + 5log3 y
log5 (3y)/fourth root of 2x
ANSWER: log5 3 + log5 y - 1/4log5 2 + 1/4log5 x
log6 cube root of (2y)/x^2
ANSWER: 1/3log6 2 + 1/3log6 y - 2/3 log6 x
logx 5a^3b^2c^4
ANSWER: logx 5 + 3logx a + 2logx b + 4logx c
logx (cube root of a^2b^2)/square root of c
ANSWER: 2/3logx a + 2/3logx b - 1/2logx c
loga (x^3)/5y
ANSWER: 3loga x - loga 5 + loga y
log10 square root of (2x)/y
ANSWER: 1/10log10 2 + 1/10log x - 1/10log10 y
log3 (square root of ac^2)/b
ANSWER: 1/2log3 a + log3 c - log3 b
log2 (fourth root of a^3b^2c)/2
ANSWER: 3/4log2 a + 1/2log2 b + 1/4log2 c - log2 2
log5 [(8x)^2]/fourth root of y^3
ANSWER: 2log5 * + 2log5 x - 3/4log5 y
Math Homework 9/24/12
ReplyDelete1.3^x+1=5^2x-3
xlog3+log3=2xlog-3log5
xlog3-2xlog5=-3log5-log3
x(log3-2log5)=-3log5-log3
Answer: x=-3log5-log3/log3-2log5
2.5^2x-3=7^x
2xlog5-3log5=xlog7
2xlog5-xlog7=3log5
x(2log5-log7)=3log5
Answer: x=3log5/2log5-log7
3.3^x-1=5^x
xlog3-log3=xlog5
xlog3-xlog5=log3
x(log3-log5)=log3
Answer: x=log3/log3-log5
4.7^2x=5^x+1
2xlog7=xlog5+log5
2xlog7-xlog5=log5
x(2log7-log5)=log5
Answer: x=log5/2log7-log5
5.7^2x-1=316
2xlog7-log7=log316
2xlog7=log316+log7
Answer: x=log316+log7/2log7
6.4^x-2=89
xlog4-2log4=log89
xlog4=log89+2log4
Answer: x=log89+2log4/log4
7.5^x+1=24
xlog5+log5=log24
xlog5=log24-log5
Answer: x=log24-log5/log5
8.4^x=19
xlog4=log19
Answer:x=log19/log4
9.6^3x+1=243
3xlog6=log243-log6
Answer: x=log243-log6/3log6
10.3^x+4=101
xlog3+4log3=log101
xlog3=log101-4log3
Answer: log101-4log3/log3
Math and I
ReplyDeleteWhen I experience difficulty in solving Math problems, I tend to complain and wonder about the use of Math in my life. Come to think of it, I realized that in life, there are lots of applications of Mathematical principles.
In the morning, when I hear my alarm clock, I estimate how much time do I have to sleep a little longer. When I take a shower, I can think how much gallon of water do I consume and how many liters there are in the gallons of water that I consume. As I shampoo my hair, I think about how many times can I wash my hair with a 200ml bottle of shampoo and how long will my bar of soap last. At breakfast time, I have to watch my calorie intake because I’m watching my weight. On my way to school, I would watch the speedometer of our car and know the distance from our house to school and find out how much time does it take for me to travel.
With all these preparations before coming to school, I have set my mood to attend my math class. I pay attention and do my best to understand the lessons that my teacher gives us and try to solve the problems as much as I can.
I think Mathematical skills are needed in other subjects, most especially in Science, TLE and even Music. Of course, I should know how to average my scores in all my subjects so I’ll be aware of how my grades are.
When I get home, I do my homework in Math. As I encounter difficult problems, I begin to ponder about the importance of Math in my life. I don’t even plan to take up engineering or other courses that require higher Mathematics. But I have to get a high grade in this subject. What then should I do to overcome this weakness in Math? Sometimes, I sleep really late because of it and cry over it but I need to be more persevering in order to at least reach my expectations if not to surpass it. Perhaps, I should begin to like it, and eventually enjoy it, and treat it like a game. I realized that my mind is exercised to solve difficult problems so that when I grow older, I will able to solve difficult problems in life.
Alexandra Cuartero
ReplyDelete10 - Pascal
Project In Math
Mathematics has always been a subject in school I really enjoyed even when it was hard. It is my favorite because I never have difficulty with it and always get good marks in tests.
My earliest memories of math are my second grade in elementary. Prior to this age, the memories of math I have are flashcards, and these tests my parents would make up for me to take while at home. It felt very rewarding every time I solved a problem correctly. From that day forward I have permanently put in my mind that math was easy. As time passed by my curiosity and desire to excel at new things have helped me develop a new love for math.
I was first introduce to algebra during my sixth grade because of the enrichment classes that our school gave us. I remember hearing rumors from the freshmen about the difficulties of algebra. Little did I know, I would love algebra in the future. A great part of the reason why I love algebra is because math is like a puzzle. For me, puzzles are exciting and challenging at the same time and I am a student who never turns her back on challenges. This is when I started believing that math is not just about finding the correct answer, but also the process of discovering.
While entering high school, math changed drastically. The high school math consisted of new terms, new formulas and new numbers that I have never seen before. It was overwhelming at first, but I was fortunate enough to have amazing teachers to guide me through them. As I continue my studies I have learned how every concept requires special attention and focus.
The wonderful thing about Mathematics is that, besides some formula, there is nothing else to remember. Every step in solving a problem is done logically. Other subjects such as History and Geography require a lot of memory work. Remembering dates and other facts is hard work compared with the ease and simplicity of mathematical reasoning.
To me, the skills you learn from Mathematics are very useful in your every day life. It is a study that shows you step-by-step methods to solve any mathematical equation. To understand math, not only do you need to know how to solve the problem step-by- step, but you also need to understand the reasons why you are solving it the way you are. Mathematics teaches us how we can come up with a solution to every problem. The only true thing I ever picked up from my math teachers was the enthusiasm to learn and the enthusiasm in “getting it”.
“Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.” -Albert Einstein
MATH AND I
ReplyDeleteMath Project for Second Quarter
Whenever someone mentions the subject "Math", people usually react in a violent manner. A lot of students see it as the most difficult subject in school. Although I do agree. Math is quite difficult. It's not easy to learn one Math topic to another. Although for some professionals, it would just be a piece of cake. But these kinds of people are rare. Not everyone can appreciate Math the way they do.
In my opinion, Math is a vast subject. Like I've said, it's not easy to learn one topic to another. But if you try to understand it, it's actually very simple. Some solutions may be long, and some are very simple. Some topics need a bucket-load of formulas to memorize, and some only need a simple solution. Math, I believe, is complicated. Topics go from easy to difficult and back to becoming easy. It's like a cycle that never ends. But if you give enough effort to try and understand the lesson, no doubt that you'll get it in no time.
I honestly believe that Math and I have quite a complicated relationship. I love Math, and I try to understand it in any way I can. There are times when I just get it, and there are times when it's just too confusing. But when I give effort and time to listen to the lessons, we'll get along fine in the end. That's how I see Math :)
KLAUDINE S. ALEJAR
ReplyDeleteOCTOBER 1, 2012
MATH AND I
Throughout the high school years, every student has their own opinions about the subjects they like and dislike. This does not mean the literal meaning. It means that it is about their strengths and weaknesses when it comes to academics. These opinions often change throughout the time. There are certain standards in every individual in order to succeed this kind of high school life.
“Mathematics is an essential part of every high school student’s education.” This quote says it all. It explains the subject Math in eleven words. Every student learns certain lessons in math that will carry with them through life. Each of these are building blocks to help shape who we become. As a math student, I feel math has taught me not only about addition, subtraction, division... But it has taught me thinking skills and problem solving that will take me further than just math class. There are times in which you have to decide which path you will take after high school, although every path is different and you will take the skills in which you have learned in math class to a different level. When I was young, I used to say “I hate math”, although this sentence did not last long. As I was growing up, I slowly understood what math really meant and how we can apply it in real life situations. I used to say that this has nothing to do with shopping or dancing and such and that I won’t need this in the future. For my other batchmates, these are hard, most especially when you are surrounded by your best friends. Concentration is obviously needed when it comes to this matter. The dedication that this class requires teaches every student concentration. The concentration on this one course will help high school students pursue their dreams while taking other courses to achieve this. Another major influence on a high school student’s math education is the teacher. A teacher is crucial to a student’s success. The ideal teacher knows several ways to explain a certain concept. Doc Ed is an example of an ideal teacher.
Soon enough, I know that I will become successful because of math. I know that this will be a big help in my future. I just have to focus at this moment and I can’t be distracted by the things that will destroy my future.
Karl Claricia
ReplyDeleteOctober 1,2012
MATH AND I
Every student has their own strengths and weaknesses. Same goes for their own opinion regarding which subject do they like or dislike,but I would daresay that Math would be one of the most infamous subject for us students. Many would ask "wouldn't life be easier without Math?" but then I would say no. A famous mathematician once said that ""The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth" which basically means that Math is something that we humans have to understand for us to be able to know what's going on around us.
Math wasn't such a nightmare for me until I stepped into highschool, this is where everything went hard. I wouldn't say that I hate Math, it's just that I wasn't putting in much effort about it. This made me realize that we always have to put specific effort for such concepts.
I always stated that I wouldn't need Math when I grow up but I was quickly corrected by my own self and realized that Math is an essential part of our daily life. I may not see it but it is everywhere. The technologies that I use is the most perfect example for me. Such ideals made me realize that I need Math in my life,that there's nothing hard when you put special attention and focus into something that you're really eager to learn.