Evaluate log base 5 of (5)^2

Problem

(log_5)(5)

Solution

1. Identify the logarithmic property for powers, which states that (log_b)(xp)=p*(log_b)(x)

2. Apply the property to the expression by moving the exponent 2 to the front of the logarithm.

(log_5)(5)=2*(log_5)(5)

3. Evaluate the remaining logarithm using the identity (log_b)(b)=1

(log_5)(5)=1

4. Multiply the results to find the final value.

2⋅1=2

Final Answer

(log_5)(5)=2

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