Answer
2
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, $log_{\frac{2}{3}}\frac{4}{9}=2$.
We know this because $(\frac{2}{3})^{2}=\frac{2}{3}\times\frac{2}{3}=\frac{4}{9}$.
