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

1. Problem Description

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

2. Solution Steps

We are given the equation $\log_x 81 = 4$.

We can rewrite this equation in exponential form.

The general form of a logarithm is $\log_b a = c$, which can be rewritten as $b^c = a$.

Applying this to our equation, we have $x^4 = 81$.

Now, we need to find the value of $x$ that satisfies this equation.

We can take the fourth root of both sides:

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

Since $3^4 = 81$, we have

$x = 3$.

3. Final Answer

The final answer is 3.