[tex]\left( \frac{4}{9} \right)^x=\frac{81}{16} \\
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\left( \frac{4}{9} \right)^x=\frac{9^2}{4^2} \\
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\left( \frac{4}{9} \right)^x=\left(\frac{9}{4} \right)^2 \\
\\
\left( \frac{4}{9} \right)^x=\left(\frac{4}{9} \right)^{-2} \\
\\
\boxed{x=-2}[/tex]
