#### Answer

$x=-4$

#### Work Step by Step

In exponential form, the given logarithmic equation, $
\log_2(8-6x)=5
,$ is equivalent to
\begin{array}{l}\require{cancel}
8-6x=2^5
.\end{array}
Hence, the value of the variable that satisfies the given equation is
\begin{array}{l}\require{cancel}
8-6x=32
\\\\
-6x=32-8
\\\\
-6x=24
\\\\
x=\dfrac{24}{-6}
\\\\
x=-4
.\end{array}