1. The problem is to convert the exponential equation $3^x = 81$ into its equivalent logarithmic form. 2. Recall the definition of logarithms: If $a^x = b$, then the logarithmic form is $\log_a(b) = x$. 3. In this problem, $a = 3$, $b = 81$, and the unknown exponent is $x$. 4. Applying the definition, we write the logarithmic form as: $$\log_3(81) = x$$ 5. To verify, note that $81 = 3^4$, so $x = 4$. 6. Therefore, the logarithmic equation equivalent to $3^x = 81$ is: $$\log_3(81) = x$$