Solve the logarithmic equation. \[ \log _{4} x=4 \] \[ x=\square \] (Simplify your answer. Type an exact answer, using $e$ as needed.)

Step 1 ：The logarithmic equation is in the form \(\log_b a = n\), which can be rewritten in exponential form as \(b^n = a\). In this case, \(b\) is 4, \(n\) is 4, and \(a\) is \(x\). So, we can rewrite the equation as \(4^4 = x\).

Step 2 ：\(b = 4\)

Step 3 ：\(n = 4\)

Step 4 ：\(x = 256.0\)

Step 5 ：The solution to the logarithmic equation \(\log _{4} x=4\) is \(x=\boxed{256}\).