Write the equation in equivalent logarithmic form.
What is the equivalent logarithmic form?
\[
6=216^{\frac{1}{3}}
\]

Answer

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Answer

So, the equivalent logarithmic form of the given equation is \(\boxed{\log_{216}(6) = \frac{1}{3}}\).

Steps

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 \(\boxed{\log_{216}(6) = \frac{1}{3}}\).