To solve the equation \(3^x = 80\) for \(x\), we can take the logarithm of both sides. Using logarithm properties, we have:
\[ x \cdot \log(3) = \log(80) \]
Now, we can solve for \(x\):
\[ x = \frac{\log(80)}{\log(3)} \]
Using a calculator to find \(\log(80)\) and \(\log(3)\):
\[ \log(80) \approx 1.9031 \] \[ \log(3) \approx 0.4771 \]
Now, substitute these values into the equation:
\[ x \approx \frac{1.9031}{0.4771} \approx 3.98 \]
Rounding to the nearest hundredth, we find:
\[ \boxed{3.98} \]