Evaluate log base 2 of 1/256

Problem

(log_2)(1/256)

Solution

1. Rewrite the fraction as a power of the denominator.

1/256=256(−1)

2. Express the number 256 as a power of 2 by identifying that 2=256

256=2

3. Substitute this power back into the expression using the power of a power rule (am)n=a(m*n)

1/256=(2)(−1)=2(−8)

4. Apply the logarithm property (log_b)(bx)=x to evaluate the expression.

(log_2)(2(−8))=−8

Final Answer

(log_2)(1/256)=−8

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