Answer
$x=-4$
Work Step by Step
We are given the equation $3^{x}=\frac{1}{81}$. First, we must write both sides using the same base.
$3^{x}=3^{-4}=\frac{1}{81}$
Next, we must take the natural log of both sides.
$ln(3^{x})=ln(3^{-4})$
$xln(3)=-4ln(3)$
Divide both sides by $ln(3)$.
$x=-4$
