Answer :
[tex]log_{\frac{2}{3}}\frac{9}{4}=x^3\\
\\
\left(\frac{2}{3}\right)^x+3=\frac{9}{4}\\
\\
\left(\frac{2}{3}\right)^{x+3}=\left(\frac{2}{3}\right)^{-2}\\
\\
x+3=-2\\
\\
x=-2-3\\
\\
\boxed{x=-5}[/tex]
[tex]log_{ \frac{2}{3} } \frac{9}{4} =x+3\\\\log_{ \frac{2}{3} }( \frac{2}{3})^{-2} =x+3\\\\-2=x+3\\\\-x=3+2\\\\-x=5\ /\cdor(-1)\\\\x=-5[/tex]