Posted by Helper on Wednesday, March 9, 2011 at 12:24am.
I'm working on logarithmic equations and I'm stuck on how my book arrives at the next step.
First, they use the change of base formula on,
log(sqrt(2))(x^3 - 2)
(sqrt(2)) is the base,changing to base 2
log(sqrt(2))(x^3 - 2)=
log2(x^3 - 2)/(log2(sqrt(2))
I understand that part.
The next step, the book has
log2(x^3 - 2)/(log2(sqrt(2))=
2 log2(x^3 - 2)
How did they get = 2 log2(x^3 - 2)??
I tried applying the different rules but I just can't get how they arrive at
= 2 log2(x^3 - 2)??
Please help. Thanks in advance.
- Logarithms - Reiny, Wednesday, March 9, 2011 at 7:40am
look at the part log2 √2
let x = log2 √2
then 2^x = √2
2^x = 2^(1/2)
x = 1/2
so log2(x^3 - 2)/(log2(sqrt(2))
= log2(x^3 - 2)/(1/2)
= 2log2(x^3 - 2)
- Logarithms - Helper, Wednesday, March 9, 2011 at 12:40pm
Thanks so much Reiny.
- Logarithms - Helper, Wednesday, March 9, 2011 at 1:36pm
Now, I feel stupid.
I guess I should not work so late at night.
I tried all these rules when all I needed to do was simplify log2√2 using the basic definition/relationship !!
Thanks again. I don't remember learning logs some 40 years ago in HS and teaching myself.
Glad tutors like yourself take time to help, even with obvious (stupid) questions such as mine was.
Answer this Question
- Math Help please!! - Could someone show me how to solve these problems step by ...
- Pre-Calculus - Laws of Logarithms Without using a calculator use the change of ...
- Precalculus - This is for solving exponential/logarithmic functions: (This is a ...
- math - Use the Laws of logarithms to rewrite the expression log(base 2)(11x(x-9...
- Calculus - Please look at my work below: Solve the initial-value problem. y'' + ...
- TRig WIth LoGs help1!! - i have problem i can't solve and the book is no help.. ...
- MATH - I need to simply this equation, but I got stuck. h/(4-sqrt(16+h)) = y ...
- math(Please help) - 1) use the properties of logarithms to simplify the ...
- algebra,math,help - Use Property 2 to simplify each of the following radical ...
- Math - The problem I have to solve is log with base 2 ^6 multiply by log base 6...