Answer
$x=-3$
Work Step by Step
We are given the equation $(\frac{4}{3})^{x}=\frac{27}{64}$. First, we must write both sides using the same base.
$(\frac{4}{3})^{x}=(\frac{4}{3})^{-3}=\frac{27}{64}$
Note that $(\frac{4}{3})^{-3}=\frac{1}{(\frac{4}{3})^{3}}=\frac{1}{\frac{64}{27}}=\frac{27}{64}$.
Next, we must take the natural log of both sides.
$ln((\frac{4}{3})^{x})=ln((\frac{4}{3})^{-3})$
$xln(\frac{4}{3})=-3ln(\frac{4}{3})$
Divide both sides by $ln(\frac{4}{3})$.
$x=-3$