Question

If $4^{{\log }_{2}2x}=36$, then the value of $x$ is equal to

Answer 1

$4^{{\log }_{2}2x}=36$
$\Rightarrow {\left(2x\right)}^{{\log }_{2}4}=36[\because a^{{\log }_{b}c}=c^{{\log }_{b}a}]$
$\Rightarrow {\left(2x\right)}^{{\log }_2{2}^2}=(2x{)}^{2{\log }_{2}2}=36$ $[\because \log a^m=m\log a]$
$\Rightarrow 4x^2=36\Rightarrow x=3$ $[\because {\log }_{a}a=1]$