Answer
$x=\frac{4}{9}$
Work Step by Step
If $b\gt0$ and $b\ne1$, then $y=log_{b}x$ means $x=b^{y}$ for every $x$ and every real number $y$.
Therefore, $log_{\frac{2}{3}}x=2$ is equivalent to $(\frac{2}{3})^{2}=x$.
$x=\frac{2}{3}\times\frac{2}{3}=\frac{2\times2}{3\times3}=\frac{4}{9}$
