Evaluate log base 6 of 95

Problem

(log_6)(95)

Solution

1. Identify the expression as a logarithm with base 6 and argument 95.

2. Apply the change of base formula to convert the expression into a form that can be calculated using common logarithms (base 10) or natural logarithms (base e.

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

4. Substitute the values into the formula.

(log_6)(95)=ln(95)/ln(6)

5. Calculate the numerical values of the natural logarithms.

ln(95)≈4.553877

ln(6)≈1.791759

6. Divide the results to find the final decimal approximation.

4.553877/1.791759≈2.541567

Final Answer

(log_6)(95)≈2.541567

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