Step 1 :Given the equation in exponential form: \(6=216^{\frac{1}{3}}\).
Step 2 :The exponential form is `b = a^x`, where `b` is the base, `a` is the result, and `x` is the exponent.
Step 3 :The equivalent logarithmic form is `log_b(a) = x`.
Step 4 :Applying this to the given equation, we get `log_216(6) = 1/3`.
Step 5 :So, the equivalent logarithmic form of the given equation is \(\boxed{\log_{216}(6) = \frac{1}{3}}\).