SOLUTION: Evaluate: log(subscript 4) 32. thanks.

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Question 201588: Evaluate: log(subscript 4) 32. thanks.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%284%2C%2832%29%29 Start with the given expression.


%28log%2810%2C%2832%29%29%29%2F%28log%2810%2C%284%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%5E5%29%29%29%2F%28log%2810%2C%288%29%29%29 Rewrite 32 as 2%5E5


%28log%2810%2C%282%5E5%29%29%29%2F%28log%2810%2C%282%5E2%29%29%29 Rewrite 4 as 2%5E2


%285%2Alog%2810%2C%282%29%29%29%2F%28log%2810%2C%282%5E2%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


%285%2Alog%2810%2C%282%29%29%29%2F%282%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.


%285%2Across%28log%2810%2C%282%29%29%29%29%2F%282%2Across%28log%2810%2C%282%29%29%29%29 Cancel out the common terms.


5%2F2 Simplify


So log%284%2C%2832%29%29=5%2F2