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 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**, 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.

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