SOLUTION: 8 to what power is 1/16th?

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Question 562470: 8 to what power is 1/16th?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
8 to what power is 1/16th?
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1/16 (not 1/16th) = 2^-4
8 = 2^3 --> 2 = 8^(1/3)
%288%5E%281%2F3%29%29-4+=+1%2F16
8%5E%28-4%2F3%29+=+1%2F16
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You can use logs and the base change formula:
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8%5Ex+=+1%2F16
x*log(8) = log(1/16)
x = log(1/16)/log(8)
x = -4/3