Evaluate log base 5 of fifth root of 25

Problem

(log_5)(√(5,25))

Solution

1. Rewrite the radical expression using a fractional exponent.

√(5,25)=25(1/5)

2. Express the base of the power as a power of 5.

25=5

3. Substitute this back into the expression and apply the power of a power rule.

(5)(1/5)=5(2/5)

4. Apply the logarithm property (log_b)(bx)=x to evaluate the expression.

(log_5)(5(2/5))=2/5

Final Answer

(log_5)(√(5,25))=2/5

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