#### Answer

$x=-59$

#### Work Step by Step

In exponential form, the given logarithmic equation, $
\log_5(7-2x)=3
,$ is equivalent to
\begin{array}{l}\require{cancel}
7-2x=5^3
.\end{array}
Hence, the value of the variable that satisfies the given equation is
\begin{array}{l}\require{cancel}
7-2x=125
\\\\
-2x=125-7
\\\\
-2x=118
\\\\
x=\dfrac{118}{-2}
\\\\
x=-59
.\end{array}