The problem asks us to solve the logarithmic equation $\log_x 81 = 4$ for $x$.

1. Problem Description

The problem asks us to solve the logarithmic equation $\log_x 81 = 4$ for $x$.

2. Solution Steps

We can rewrite the logarithmic equation in exponential form:

$\log_x 81 = 4$ is equivalent to $x^4 = 81$.

To find $x$, we need to take the fourth root of both sides of the equation:

$x = \sqrt[4]{81}$

Since $81 = 3^4$, we have:

$x = \sqrt[4]{3^4}$

$x = 3$

3. Final Answer

The solution is $x = 3$.