SOLUTION: How do I get the solution to 1/3log(x+2)=log8

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Question 674118: How do I get the solution to
1/3log(x+2)=log8
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
Notice log(a^b) = b*log(a) by our power property of logarithms.
We have %281%2F3%29log%28x%2B2%29 but that is log%28%28%28x%2B2%29%5E%281%2F3%29%29%29
So, log%28%28%28x%2B2%29%5E%281%2F3%29%29%29+=+log%288%29
Log is usually noted as base 10, so exponentiate both sides by 10.
10^log((x+2)^(1/3)) = 10%5E%28log%288%29%29
%28x%2B2%29%5E%281%2F3%29+=+8
Cube both sides.
x%2B2+=+8%5E3
x%2B2+=+512
x+=+510
Check:
(1/3) * log(510+2) = (1/3) log(512) = .9031
log(8) = .9031