SOLUTION: Evaluate the following: {{{(log(sqrt(2),31))(log(3,46.7))}}}

Algebra ->  Exponents -> SOLUTION: Evaluate the following: {{{(log(sqrt(2),31))(log(3,46.7))}}}      Log On


   

Question 842672: Evaluate the following:
%28log%28sqrt%282%29%2C31%29%29%28log%283%2C46.7%29%29
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Use the Change of Base Formula for both logarithmic factors. The product will start like this, if you choose base ten:


and then
%282%2Alog%2810%2C31%29%2Flog%2810%2C2%29%29%28log%2810%2C46.7%29%2Flog%2810%2C3%29%29
You should be comfortable with the steps still needing to be done.



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Change of Base Formula: log%28a%2Cr%29=log%28b%2Cr%29%2Flog%28b%2Ca%29