Evaluate log base 16 of 15

Problem

(log_16)(15)

Solution

1. Apply the change of base formula to rewrite the expression 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 natural logarithms.

(log_16)(15)=ln(15)/ln(16)

3. Calculate the values of the logarithms.

ln(15)≈2.70805

ln(16)≈2.77259

4. Divide the results to find the decimal approximation.

2.70805/2.77259≈0.97672

Final Answer

(log_16)(15)≈0.97672

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