Step 1 :The question is asking to convert the exponential equation to a logarithmic form.
Step 2 :The general form of a logarithm is \(\log_b(a) = c\), which is equivalent to \(b^c = a\).
Step 3 :In this case, \(b = 4\), \(c = 4\), and \(a = 256\).
Step 4 :So, the logarithmic form of the equation \(4^4 = 256\) is \(\log_4(256) = 4\).
Step 5 :\(\boxed{\log _{4}(256)=4}\) is the final answer.