Answer
$x=22$
Work Step by Step
Since $y=b^x$ is equivalent to $\log_by=x$, the given equation, $
\log_8(3x-2)=2
,$ is equivalent to
\begin{array}{l}\require{cancel}
3x-2=8^2
.\end{array}
Using the properties of inequality, the solution to the equation above is
\begin{array}{l}\require{cancel}
3x-2=64
\\\\
3x=64+2
\\\\
3x=66
\\\\
x=\dfrac{66}{3}
\\\\
x=22
.\end{array}
