Write in logarithmic form.
What is the equivalent logarithmic form?
\[
4^{4}=256
\]
\[
\log _{4}(\square)=\square
\]
(Simplify your answers. Type integers or fractions.)

Answer

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Answer

\(\boxed{\log _{4}(256)=4}\) is the final answer.

Steps

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.