1. The problem is to solve the logarithmic equation $\log_x 64 = 3$. 2. Recall the definition of logarithm: $\log_a b = c$ means $a^c = b$. 3. Using this definition, rewrite the equation as an exponential equation: $$x^3 = 64$$ 4. To solve for $x$, take the cube root of both sides: $$x = \sqrt[3]{64}$$ 5. Since $64 = 4^3$, we have: $$x = 4$$ 6. Therefore, the solution to the equation $\log_x 64 = 3$ is $x = 4$.