Evaluate log base 6 of 25

Problem

(log_6)(25)

Solution

1. Identify the expression as a logarithm with base 6 and argument 25.

2. Apply the change of base formula to rewrite the expression using natural logarithms or common logarithms.

(log_b)(a)=ln(a)/ln(b)

3. Substitute the values a=25 and b=6 into the formula.

(log_6)(25)=ln(25)/ln(6)

4. Simplify the numerator by recognizing that 25=5 and applying the power rule for logarithms, ln(xy)=y*ln(x)

ln(25)=ln(5)=2*ln(5)

5. Combine the results to express the final exact value.

(log_6)(25)=(2*ln(5))/ln(6)

Final Answer

(log_6)(25)=(2*ln(5))/ln(6)

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