Answer
$x=1$
Work Step by Step
The given expression is
$\Rightarrow 5^x=5^{3x-2}$
Equate the exponents.
$\Rightarrow x=3x-2$
Add $2-x$ to each side.
$\Rightarrow x+2-x=3x-2+2-x$
Simplify.
$\Rightarrow 2=2x$
Divide each side by $2$.
$\Rightarrow \frac{2}{2}=\frac{2x}{2}$
Simplify.
$\Rightarrow 1=x$.
