Evaluate log base 5 of 13

Problem

(log_5)(13)

Solution

1. Identify the expression as a logarithm with base 5 and argument 13

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

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

3. Substitute the values into the formula.

(log_5)(13)=ln(13)/ln(5)

4. Calculate the numerical values of the natural logarithms.

ln(13)≈2.564949

ln(5)≈1.609438

5. Divide the results to find the decimal approximation.

2.564949/1.609438≈1.593654

Final Answer

(log_5)(13)=ln(13)/ln(5)≈1.5937

Want more problems? Check here!