Find the logarithm. \[ \log _{3} \sqrt[5]{3} \]

Step 1 ：We are given the logarithm \(\log _{3} \sqrt[5]{3}\).

Step 2 ：The logarithm of a number is the exponent to which another fixed number, the base, must be raised to produce that number.

Step 3 ：In this case, the base is 3 and the number is the fifth root of 3. We need to find the exponent that satisfies this equation.

Step 4 ：We know that the nth root of a number x can be written as \(x^{1/n}\). So, the fifth root of 3 can be written as \(3^{1/5}\).

Step 5 ：The logarithm base 3 of \(3^{1/5}\) is 1/5, because 3 raised to the power of 1/5 gives us \(3^{1/5}\).

Step 6 ：Final Answer: The logarithm base 3 of the fifth root of 3 is \(\boxed{\frac{1}{5}}\).