SOLUTION: Evaluate: log (subscript 8)(1/16) Thanks.

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Question 201587: Evaluate: log (subscript 8)(1/16) Thanks.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%288%2C%281%2F16%29%29 Start with the given expression.


%28log%2810%2C%281%2F16%29%29%29%2F%28log%2810%2C%288%29%29%29 Use the change of base formula


Note: Remember the change of base formula is log%28b%2C%28x%29%29=log%2810%2C%28x%29%29%2Flog%2810%2C%28b%29%29



%28log%2810%2C%282%5E%28-4%29%29%29%29%2F%28log%2810%2C%288%29%29%29 Rewrite 1%2F16 as 2%5E%28-4%29


%28log%2810%2C%282%5E%28-4%29%29%29%29%2F%28log%2810%2C%282%5E3%29%29%29 Rewrite 8 as 2%5E3


%28-4%2Alog%2810%2C%282%29%29%29%2F%28log%2810%2C%282%5E3%29%29%29 Pull down the first exponent using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


%28-4%2Alog%2810%2C%282%29%29%29%2F%283%2Alog%2810%2C%282%29%29%29 Pull down the second exponent using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


Highlight the common terms.


%28-4%2Across%28log%2810%2C%282%29%29%29%29%2F%283%2Across%28log%2810%2C%282%29%29%29%29 Cancel out the common terms.


-4%2F3 Simplify



So log%288%2C%281%2F16%29%29=-4%2F3