Answer
$x=-2$
Work Step by Step
We rewrite both sides, so that the base is $\frac{3}{2}$ on both sides.
Left side: $\frac{2}{3}^x$.
By the law of exponents:$\frac{1}{a}^x=a^{-x}$
$\frac{2}{3}^x=\frac{3}{2}^{-x}$
Right side: $\frac{9}{4}=\frac{3}{2}^2$
Thus, the given equation is equivalent to:
$\frac{3}{2}^{-x}=\frac{3}{2}^2$
Since the bases are the same, we set the exponents equal:
$-x=2
\\-1(-x)=-1(2)
\\x=-2$
