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Chapter 12: Problem 26

Evaluate each expression without using a calculator. $$\log _{6} \frac{1}{6}$$

Short Answer

Expert verified
The evaluation of \(\log _{6} \frac{1}{6}\) is -1.

Step by step solution

01

Understand the problem

We wish to evaluate the expression \(\log _{6} \frac{1}{6}\). This is equivalent to finding a power to which 6 must be raised to give us the number \(\frac{1}{6}\).\The decimal result is not required in this question. Instead, an exact value in integer or fractional form is needed.
02

Apply Logarithm Rule

Any positive number raised to the power -1 results in its reciprocal. Therefore, based on this fact, 6 raised to the power of -1 gives us \(\frac{1}{6}\). So the power to which 6 must be raised to get \(\frac{1}{6}\) is -1.
03

Final Answer

Therefore, the expression \(\log _{6} \frac{1}{6}\) equals to -1.

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