Write in logarithmic form. \[ 8^{3}=512 \] The logarithmic form of $8^{3}=512$ is $\square$. (Use integers or fractions for any numbers in the equation.)

Step 1 ：The given equation is in exponential form: \(8^{3}=512\).

Step 2 ：The general form of a logarithmic equation is \(\log_{b}(a) = c\), which is equivalent to the exponential form \(b^{c} = a\). Here, \(b\) is the base, \(a\) is the result and \(c\) is the exponent.

Step 3 ：In the given equation, 8 is the base, 512 is the result and 3 is the exponent. So, we can directly substitute these values into the logarithmic form.

Step 4 ：The logarithmic form of \(8^{3}=512\) is \(\log_{8}{512} = 3\).

Step 5 ：\(\boxed{\log_{8}{512} = 3}\) is the final answer.