Evaluate log base 15 of 1250

Problem

(log_15)(1250)

Solution

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

(log_15)(1250)=(log_)(1250)/(log_)(15)

2. Calculate the values of the logarithms in the numerator and the denominator.

(log_)(1250)≈3.09691

(log_)(15)≈1.17609

3. Divide the results to find the decimal approximation of the original expression.

3.09691/1.17609≈2.63322

Final Answer

(log_15)(1250)≈2.63322

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