Change of Base Worksheets
Use explicitly stated exponential and logarithmic models and interpret their parameters.
Before you begin
Evaluate functions, solve for variables and use exponential/logarithmic inverses.
Worked example
Evaluate log base 3 of 27 using the change-of-base formula.
- Write ln(27) / ln(3).
- Since 27 = 3^3, the ratio is 3.
Answer: 3
Check your result using the method in the example before moving to the next question.
Choose your level
These sets use the same exercise types and number ranges across level labels. Choose a fresh set for additional practice.
- Easy: Start with the preview and follow the worked example.
- Medium: Practice the same exercise types with a fresh numbered set.
- Hard: Use another set to practice explaining and checking your answers.
Questions and answer calculations checked on 2026-09-17. How we check worksheets. Free for personal and classroom use.
Preview and print an easy set
Try six questions below, or choose a full set at your level.
1
Evaluate log base 2 of 4 using the change-of-base formula.
2
Evaluate log base 4 of 4 using the change-of-base formula.
3
Evaluate log base 5 of 125 using the change-of-base formula.
4
Evaluate log base 4 of 16 using the change-of-base formula.
5
Evaluate log base 4 of 256 using the change-of-base formula.
6
Evaluate log base 5 of 625 using the change-of-base formula.
Answer Key
1. 22. 13. 34. 25. 46. 4