Evaluate log base 5 of 1/25

Problem

(log_5)(1/25)

Solution

1. Rewrite the fraction using a base of 5 by recognizing that 25=5^2

1/25=1/5^2

2. Apply the property of negative exponents, which states that 1/(a^n)=a^(−n)

1/5^2=5^(−2)

3. Substitute the new expression back into the logarithm.

(log_5)(5^(−2))

4. Use the logarithm power property (log_b)(b^x)=x to evaluate the expression.

(log_5)(5^(−2))=−2

Final Answer

(log_5)(1/25)=−2

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