Answer
$x=22$
Work Step by Step
Since $\log_b x=y$ implies $b^y=x$, then,
\begin{array}{l}
\log_8 (3x-2)=2
\\\\
3x-2=8^2
\\\\
3x-2=64
\\\\
3x=66
\\\\
x=22
.\end{array}
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