To rewrite \((\frac{1}{3})^{-4}\) as a logarithmic equation, first, we simplify the expression.
\[ (\frac{1}{3})^{-4} = 3^4 \]
Calculating \(3^4\):
\[ 3^4 = 81 \]
Now, we can express this in logarithmic form. The expression \(3^4 = 81\) can be written as:
\[ \log_3(81) = 4 \]
So, the logarithmic equation corresponding to \((\frac{1}{3})^{-4}\) is:
\[ \log_3(81) = 4 \]