Posted by Helper on .
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,
look at the part log_{2} √2
let x = log_{2} √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,
Thanks so much Reiny.

Logarithms 
Helper,
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.