Answer
$x=5$
Work Step by Step
Since $\log_b x=y$ is equivalent to $b^y=x$, then,
\begin{array}{l}
\log_5 (x^2-4x)=1\\\\
x^2-4x=5^1\\\\
x^2-4x-5=0\\\\
(x-5)(x+1)=0\\\\
x=\{-1,5\}
.\end{array}
Since the domain of the logarithmic function is the set of all positive numbers, then $
x=5
$.
