Evaluate log base 5 of 121

Problem

(log_5)(121)

Solution

1. Identify the expression as a logarithm with base 5 and argument 121.

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

3. Substitute the formula (log_b)(a)=ln(a)/ln(b)

4. Rewrite the argument 121 as 11 if further simplification of the logarithmic form is desired.

5. Apply the power rule for logarithms, ln(xk)=k*ln(x) to move the exponent in front of the natural log.

Final Answer

(log_5)(121)=(2*ln(11))/ln(5)

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