SOLUTION: Evaluate: log8^4

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Question 192191: Evaluate: log8^4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%288%2C%284%29%29 Start with the given expression


%28log%2810%2C%284%29%29%29%2F%28log%2810%2C%288%29%29%29 Use the change of base formula


%28log%2810%2C%282%5E2%29%29%29%2F%28log%2810%2C%282%5E3%29%29%29 Rewrite 4 as 2%5E2 and 8 as 2%5E3


%282%2Alog%2810%2C%282%29%29%29%2F%283%2Alog%2810%2C%282%29%29%29 Pull down the exponents


%282%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.


2%2F3 Simplify


So log%288%2C%284%29%29=2%2F3