Answer
$x=\dfrac{5}{8}$
Work Step by Step
The value of $x$ in the expression $
\log_4 10-\log_4 x =2
$ is
\begin{array}{l}
\log_4 \dfrac{10}{x}=2
\text{...use properties of logarithms}
\\\\
4^2=\dfrac{10}{x}
\text{...convert to exponential form}
\\\\
16=\dfrac{10}{x}
\\\\
16x=10
\text{...cross multiply}
\\\\
x=\dfrac{10}{16}
\\\\
x=\dfrac{5}{8}
.\end{array}