Answer
$x=-2$
Work Step by Step
Expressing the terms on both sides of the equal sign in the same base so that the exponents can be equated results to
\begin{array}{l}
\dfrac{1}{81}=3^{2x}
\\\\
\dfrac{1}{3^4}=3^{2x}
\\\\
3^{-4}=3^{2x}
\\\\
-4=2x
\\\\
x=-2
.\end{array}
