Question

Solve:$\sqrt{lo{g}_{4}4}+{log}_4\sqrt{\frac{2}{x}}=2$

Answer 1

$\sqrt{{\log }_{4}4}+{\log }_4\sqrt{\frac{2}{x}}=2$

$\Rightarrow \sqrt{1}+{\log }_4\sqrt{\frac{2}{x}}=2$

$\Rightarrow 1+{\log }_4\sqrt{\frac{2}{x}}=2$

$\Rightarrow {\log }_4\sqrt{\frac{2}{x}}=2-1=1$

$\Rightarrow \sqrt{\frac{2}{x}}=4$

$\Rightarrow \frac{2}{x}=16$

$\Rightarrow 16x=2$

$\Rightarrow x=\frac{2}{16}=\frac{1}{8}$

$\therefore x=\frac{1}{8}$