1. The problem asks to rewrite the exponential equation $$3^{-4} = \frac{1}{81}$$ as a logarithmic equation. 2. Recall the definition of logarithms: If $$a^x = b$$, then $$\log_a(b) = x$$. 3. Here, $$a = 3$$, $$x = -4$$, and $$b = \frac{1}{81}$$. 4. Applying the logarithm definition, we get: $$\log_3\left(\frac{1}{81}\right) = -4$$ 5. This is the logarithmic form of the given exponential equation. 6. Note that $$81 = 3^4$$, so $$\frac{1}{81} = 3^{-4}$$, confirming the correctness of the logarithmic equation.