Answer
$x=\frac{8}{9}$
Work Step by Step
We are given that $8^{3x-2}=4$. Both of these numbers are powers of 2, so we can rewrite the equation as $(2^{3})^{3x-2}=2^{9x-6}=2^{2}$.
From the uniqueness of $b^{x}$, we know that $b^{x}=b^{y}$ is equivalent to $x=y$ (when $b\gt0$ and $b\ne1$).
Therefore, $9x-6=2$. To solve for x, add 6 to both sides.
$9x=8$
Divide both sides by 9.
$x=\frac{8}{9}$
