Evaluate log base 0.5 of 128

Problem

(log_0.5)(128)

Solution

1. Identify the base and the argument of the logarithm. The base is 0.5 and the argument is 128

2. Rewrite the base and the argument as powers of 2

(log_0.5)(128)=(log_2(−1))(2)

3. Apply the change of base formula or the property (log_bn)(am)=m/n*(log_b)(a)

(log_2(−1))(2)=7/(−1)*(log_2)(2)

4. Simplify the expression using the identity (log_b)(b)=1

−7⋅1=−7

Final Answer

(log_0.5)(128)=−7

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