Evaluate.
\[
\log _{2} \frac{1}{8}
\]
\[
\log _{2} \frac{1}{8}=\square
\]

Answer

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Answer

Final Answer: \( \log _{2} \frac{1}{8} = \boxed{-3} \)

Steps

Step 1 ：Evaluate the expression \( \log _{2} \frac{1}{8} \).

Step 2 ：We know that \( \log _{b} a = n \) if and only if \( b^n = a \).

Step 3 ：So, we need to find a number \( n \) such that \( 2^n = \frac{1}{8} \).

Step 4 ：We know that \( 2^{-3} = \frac{1}{8} \).

Step 5 ：Therefore, \( n = -3 \).

Step 6 ：So, \( \log _{2} \frac{1}{8} = -3 \).

Step 7 ：Final Answer: \( \log _{2} \frac{1}{8} = \boxed{-3} \)