Question 1119015
prove that 27^log2=8^log3
 
Hint : take log both the sides
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Did you try it?   

They want you to use this property {{{ log((x^k)) = k*log((x)) }}}.   The key is you need to use it more than once.

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LHS:
{{{ log((27^(log((2))))) = log((2))*log((27)) = log((2))*log((3^3)) = green(3*log((2))*log((3))) }}}<br>

RHS:
{{{ log((8^(log((3))))) = log((3))*log((8)) = log((3))*log((2^3)) = 3*log((3))*log((2)) = green(3*log((2))*log((3))) }}} 

They match.