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