Answer
$x=-3$
Work Step by Step
We are given the equation $(\frac{3}{2})^{x}=\frac{8}{27}$. First, we must write both sides using the same base.
$(\frac{3}{2})^{x}=(\frac{3}{2})^{-3}=\frac{8}{27}$
Note that $(\frac{3}{2})^{-3}=\frac{1}{(\frac{3}{2})^{3}}=\frac{1}{\frac{27}{8}}=\frac{8}{27}$.
Next, we must take the natural log of both sides.
$ln((\frac{3}{2})^{x})=ln((\frac{3}{2})^{-3})$
$xln(\frac{3}{2})=-3ln(\frac{3}{2})$
Divide both sides by $ln(\frac{3}{2})$.
$x=-3$
