Evaluate log base 5 of 33

Problem

(log_5)(33)

Solution

1. Identify the expression as a logarithm with base 5 and argument 33.

2. Apply the change of base formula to convert the expression into a form that can be calculated using common logarithms (base 10) or natural logarithms (base e.

3. Use the formula (log_b)(a)=ln(a)/ln(b)

4. Substitute the values into the formula.

(log_5)(33)=ln(33)/ln(5)

5. Calculate the numerical values of the natural logarithms.

ln(33)≈3.496507

ln(5)≈1.609438

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

3.496507/1.609438≈2.1725

Final Answer

(log_5)(33)=ln(33)/ln(5)≈2.1725

Want more problems? Check here!