Answer
$x=\dfrac{11}{9}$
Work Step by Step
Express both sides of the equation with the same base. Once the bases are the same, then equate the exponents. That is,
\begin{array}{l}
8^{3x-2}=32\\\\
(2^3)^{3x-2}=2^5\\\\
2^{9x-6}=2^5\\\\
9x-6=5\\\\
9x=11\\\\
x=\dfrac{11}{9}
.\end{array}
