Evaluate log base 2 of 1/8

Problem

(log_2)(1/8)

Solution

1. Rewrite the fraction as a power of a whole number using the rule 1/(a^n)=a^(−n)

1/8=1/2^3

1/8=2^(−3)

2. Substitute the power back into the logarithmic expression.

(log_2)(2^(−3))

3. Apply the logarithm power rule (log_b)(b^x)=x

(log_2)(2^(−3))=−3

Final Answer

(log_2)(1/8)=−3

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