Advanced Math/Logarithms

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Question
log(base 10)3= a
log(base 10)2= b
Then log(base 5)6=???????
Please answer it.

Answer
10^a = 3

10^b = 2


(5^a)(2^a) = 3

(5^b)(2^b) = 2


5^b = 2^(1-b)

5^(b/(1-b)) = 2

(5^a)(5^(ab/(1-b))) = 3

5^(a/(1-b)) = 3


Multiply left sides and right sides of

5^(b/(1-b)) = 2
5^(a/(1-b)) = 3

To get

5^((a+b)/(1-b)) = 6

So log (base 5) 6 = ((a+b)/(1-b))  

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