Problem

Find the value of the logarithmic expression.
\[
\log _{6}\left(\frac{1}{216}\right)
\]

The value of the logarithmic expression $\log _{6}\left(\frac{1}{216}\right)=$

Answer

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Answer

Final Answer: The value of the logarithmic expression \(\log _{6}\left(\frac{1}{216}\right)\) is \(\boxed{-3}\).

Steps

Step 1 :Find the value of the logarithmic expression \(\log _{6}\left(\frac{1}{216}\right)\).

Step 2 :The logarithm base 6 of a number is the exponent to which 6 must be raised to get that number. In this case, we need to find the exponent to which 6 must be raised to get 1/216.

Step 3 :We know that 6 cubed is 216, so 6 to the power of -3 is 1/216.

Step 4 :Therefore, the value of the logarithmic expression is -3.

Step 5 :Final Answer: The value of the logarithmic expression \(\log _{6}\left(\frac{1}{216}\right)\) is \(\boxed{-3}\).

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