SOLUTION: Hello there, For the following problem, I am not sure if my answer is right or if the given answer is right. In the case that the given answer is correct, could someone please e

Question 118399: Hello there,
For the following problem, I am not sure if my answer is right or if the given answer is right. In the case that the given answer is correct, could someone please explain where I might have erred?
Thank you !
---
1.
=
=
=
However, the given answer is .
Found 2 solutions by jim_thompson5910, ilana:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given expression

Rewrite the logs using the change of base formula

Cancel like terms

Simplify

Combine the fractions

Break up the log using the identity

Break up the fraction

Cancel like terms

Simplify

Rewrite as

Rewrite the log using the identity

Cancel like terms

Simplify

Add the fractions

So

I checked this answer with my calculator, so you must have typed in the problem incorrectly or it might be displayed incorrectly. Double check your book to verify that you have the right problem.
Answer by ilana(307) (Show Source): You can put this solution on YOUR website!
It seems to me you are both wrong. Your last step does not work. Think of it this way: log(base2)8/log(base2)4=3/2, but 8/4=2. So just dividing does not work. To check your answers, I used the fact that log(base3)2 = log2/log3 (with any base- so the calculator uses base 10). So I did (log2/log3)*(log3rt3/log2)=log3rt3/log3=1.5
I honestly do not remember any rule that would help me get that without my calculator, but I know that the rules I used are true, so I believe the answer is 1/3.
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