## College Algebra (11th Edition)

$x=-2$
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: $-x=2 \\-1(-x)=-1(2) \\x=-2$