To simplify the equation \(\log_x 4 = 3\), we can rewrite it in exponential form. The logarithmic equation \(\log_x 4 = 3\) means that \(x\) raised to the power of \(3\) equals \(4\). This can be expressed as:
\[ x^3 = 4 \]
To solve for \(x\), we can take the cube root of both sides:
\[ x = 4^{1/3} \]
This can also be expressed as:
\[ x = \sqrt[3]{4} \]
Therefore, the simplified form of the equation \(\log_x 4 = 3\) gives us:
\[ x = \sqrt[3]{4} \]