Evaluate log base 4 of 1/4

Problem

(log_4)(1/4)

Solution

1. Identify the base and the argument of the logarithm. The base is 4 and the argument is 1/4

2. Rewrite the argument as a power of the base using the property of negative exponents, where 1/a=a(−1)

3. Apply the property 1/4=4(−1) to the expression.

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

Final Answer

(log_4)(1/4)=−1

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