Express the given equation in logarithmic form. \[ 4^{-4}=\frac{1}{256} \] The logarithmic form is (Type an equation. Use integers or fractions for any numbers in the equation.)

Step 1 ：Express the given equation in logarithmic form: \(4^{-4} = \frac{1}{256}\)

Step 2 ：Rewrite 4 as \(2^2\): \((2^2)^{-4} = \frac{1}{256}\)

Step 3 ：Simplify the exponent: \(2^{-8} = \frac{1}{256}\)

Step 4 ：Write the equation in logarithmic form: \(\log_2 \frac{1}{256} = -8\)

Step 5 ：\(\boxed{\log_2 \frac{1}{256} = -8}\)