Find the logarithm.
\[
\log _{5}\left(5^{\frac{1}{3}}\right)=
\]

Answer

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Answer

Final Answer: \(\boxed{\frac{1}{3}}\)

Steps

Step 1 ：Given the logarithm \(\log _{5}\left(5^{\frac{1}{3}}\right)\)

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

Step 3 ：In this case, the base is 5 and the number is \(5^{\frac{1}{3}}\). The exponent is what we're trying to find.

Step 4 ：Since the base and the number have the same base (5), the exponent of the number is the answer to the logarithm.

Step 5 ：So, \(\log _{5}\left(5^{\frac{1}{3}}\right) = \frac{1}{3}\)

Step 6 ：Final Answer: \(\boxed{\frac{1}{3}}\)