Answer
$x=\dfrac{5}{8}$
Work Step by Step
$\log_{4}10-\log_{4}x=2$
Combine $\log_{4}10-\log_{4}x$ as the $\log$ of a division:
$\log_{4}\dfrac{10}{x}=2$
Rewrite this equation in exponential form:
$4^{2}=\dfrac{10}{x}$
$\dfrac{10}{x}=16$
Solve for $x$:
$\dfrac{x}{10}=\dfrac{1}{16}$
$x=\dfrac{10}{16}$
$x=\dfrac{5}{8}$