Question

prove the following:
$3^{\log 4}=4^{\log 3}$

Answer 1

LHS

$3^{\log 4}=k\left(say\right)\log 3^{\log 4}=\log k\log 4\log 3=\log k\cdots \left(1\right)$

RHS

$4^{\log 3}=l\left(say\right)\log 4^{\log 3}=\log l\log 3\log 4=\log l\cdots \left(2\right)$

From $\left(1\right)\left(2\right)$

$\log k=\log ll=k{3}^{\log 4}=4^{\log 3}$

Hence proved