SOLUTION: Evaluate the following without a calculator: log8 of the 4th root of 1/2 I believe that I should be doing the 4th root of 1/2 and taking it to the 8th power?

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Question 478338: Evaluate the following without a calculator: log8 of the 4th root of 1/2
I believe that I should be doing the 4th root of 1/2 and taking it to the 8th power?
Answer by scott8148(6628)   (Show Source): You can put this solution on YOUR website!
log8 means 1/2 as a power of 8

8^(1/3) = 2 ___ 2^(-1) = 1/2 ___ so ___ 8^(-1/3) = 1/2 ___ and ___ log8(1/2) = -1/3

log8[1/2^(1/4)] = (-1/3)(1/4) = -1/12
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