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