To solve the equation \(3^x = \frac{1}{81}\), we can rewrite \(\frac{1}{81}\) in terms of base 3.
First, note that \(81\) can be expressed as a power of \(3\): \[ 81 = 3^4 \] Thus, \[ \frac{1}{81} = \frac{1}{3^4} = 3^{-4} \]
Now, we can rewrite the original equation: \[ 3^x = 3^{-4} \]
Since the bases are the same, we can set the exponents equal to each other: \[ x = -4 \]
Therefore, the solution is: \[ \boxed{-4} \]