Question

Solve the following equation:
$x^{{\log }_{4}x}=9$

Answer 1

${}_{x}lo{g}_{4}x=9\Rightarrow {log}_{4}x={log}_{x}9\Rightarrow {\left(logx\right)}^2=log9log4\Rightarrow logx=\pm 2\sqrt{\left(log3\right)\left(log2\right)}$

Therefore, $x={10}^{2\sqrt{\left(log3\right)\left(log2\right)}}$ or ${10}^{-2\sqrt{\left(\log 3\right)\left(\log 2\right)}}$