To solve the equation \( 3^x = \frac{1}{81} \), we can rewrite \( \frac{1}{81} \) as a power of 3.
First, notice that: \[ 81 = 3^4 \] Thus, we have: \[ \frac{1}{81} = \frac{1}{3^4} = 3^{-4} \]
Now, we can substitute this back into the 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: \[ \boxed{-4} \]