SOLUTION: If a=log base 10 of 2, and b= log base 10 of 3. Express log base 81 of 80 in terms of a & b without incorporating the word "log" in your expression.

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Question 253873: If a=log base 10 of 2, and b= log base 10 of 3. Express log base 81 of 80 in terms of a & b without incorporating the word "log" in your expression.
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
We have the following:
(i) log_81%2880%29
By change of base, we get
(ii) log%2880%29%2Flog%2881%29
(iii) Log%2880%29+=+log%288%2A10%29+=+log%282%5E3%2A10%29+=+3log%282%29+%2B+1
(iv) log%2881%29+=+log%283%5E4%29 = log%283%5E4%29+=+4log%283%29
substituting (iii) and (iv) into (ii) we get
(v) %283log%282%29+%2B+1%29%2F%284log%283%29%29
We were given
a=log_10(2), and b= log_10(3).
Substituting, we get
%283a+%2B+1%29%2F%284b%29