Answer
$x=\dfrac{3}{2}$
Work Step by Step
Since $\log_b m=\log_b n $ implies $m=n$, then the given equation, $
\log (7-2x)=\log 4
$, implies
\begin{align*}\require{cancel}
7-2x&=4
.\end{align*}
Using the properties of equality, the equation above is equivalent to
\begin{align*}\require{cancel}
7-4&=2x
\\
3&=2x
\\\\
\dfrac{3}{2}&=\dfrac{\cancel2x}{\cancel2}
\\\\
\dfrac{3}{2}&=x
\\\\
x&=\dfrac{3}{2}
.\end{align*}
Hence, the solution to the equation $
\log (7-2x)=\log 4
$ is $
x=\dfrac{3}{2}
$.