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.
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)
Thanks so much Reiny.
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.
To understand how the book arrived at the next step, let's break it down step by step:
Starting with:
log2(x^3 - 2)/(log2(sqrt(2)))
We can simplify the expression inside the logarithm:
log2(x^3 - 2)/(1/2)
Now, let's apply the rule of division of logarithms:
log2(x^3 - 2) * 2
Note that log2(sqrt(2)) equals 1/2, so we multiply the expression by 2 to get:
2 log2(x^3 - 2)
Therefore, the next step is:
log2(x^3 - 2)/(log2(sqrt(2))) = 2 log2(x^3 - 2)
I hope this explanation clarifies how the book arrived at the next step. If you have any more questions, feel free to ask!