Question

Solve the following equation:
$4^{\frac{1}{x}-2}=\frac{\log \sqrt{10}}{2}$

Answer 1

$4^{\frac{1}{x}-2}=\frac{log\sqrt{10}}{2}{\Rightarrow 2}^{\frac{2}{x}-4}=\frac{1}{4}\Rightarrow 2^{\frac{2}{x}-4}=2^{-2}\Rightarrow \frac{2}{x}-4=-2\Rightarrow \frac{2}{x}=2\Rightarrow x=1$