Evaluate log base 2 of 1/16

Problem

(log_2)(1/16)

Solution

1. Rewrite the fraction as a power of the base number by identifying that 16=2

1/16=1/2

2. Apply the rule for negative exponents, which states that 1/(an)=a(−n)

1/2=2(−4)

3. Substitute the power back into the logarithmic expression.

(log_2)(2(−4))

4. Use the logarithm power property (log_b)(bx)=x to simplify the expression.

(log_2)(2(−4))=−4

Final Answer

(log_2)(1/16)=−4

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