Answer
$x=\displaystyle \frac{1}{2}$
Work Step by Step
$(\displaystyle \frac{9}{16})^{x}=\frac{3}{4}\qquad \color{blue}{\text{ ...recognize } 9=3^{2}, 16=4^{2}}$
$[(\displaystyle \frac{3}{4})^{2}]^{x}=\frac{3}{4}\qquad \color{blue}{\text{ ...apply } (a^{n})^{m}=a^{nm},\quad a^{1}=a}$
$(\displaystyle \frac{3}{4})^{2x}=(\frac{3}{4})^{1}\qquad \color{blue}{\text{ ...equate the exponents } }$
$2x=1$
$x=\displaystyle \frac{1}{2}$
