Evaluate log base 5 of 3

Problem

(log_5)(3)

Solution

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

(log_b)(a)=ln(a)/ln(b)

2. Substitute the given values a=3 and b=5 into the formula.

(log_5)(3)=ln(3)/ln(5)

3. Calculate the numerical values of the logarithms using a calculator.

ln(3)≈1.098612

ln(5)≈1.609438

4. Divide the results to find the decimal approximation.

1.098612/1.609438≈0.6826

Final Answer

(log_5)(3)≈0.6826

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