## Precalculus (10th Edition)

$x=\frac{11}{3}$
We know that if $\log_a {y}=x$ then $a^x=y$. Hence, if $\log_3 {(3x-2)}=2$, then $3^2=3x-2$. Solve the equation above to obtain: \begin{align*} 9&=3x-2\\ 9+2&=3x\\ 11&=3x\\ x&=\frac{11}{3}\end{align*}