Evaluate log base 15 of 14

Problem

(log_15)(14)

Solution

1. Apply the change of base formula to rewrite the logarithm using common logarithms (base 10) or natural logarithms (base e.

(log_b)(a)=(log_c)(a)/(log_c)(b)

2. Substitute the values into the formula using the natural logarithm ln()

(log_15)(14)=ln(14)/ln(15)

3. Calculate the numerical values of the logarithms.

ln(14)≈2.639057

ln(15)≈2.708050

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

2.639057/2.708050≈0.974523

Final Answer

(log_15)(14)≈0.9745

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