Properties of Logarithms Worksheets
Evaluate exponentials and logarithms using inverse relationships, with positive log arguments.
Before you begin
Factor polynomials, use exponent laws and solve equations with domain restrictions.
Worked example
For x > 0 and y > 0, expand ln(x^4/y^3).
- The logarithm of a quotient is a difference.
- Move positive real powers down as coefficients.
Answer: 4 ln(x) − 3 ln(y)
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
For x > 0 and y > 0, expand ln(x^2/y^5).
2
For x > 0 and y > 0, expand ln(x^1/y^4).
3
For x > 0 and y > 0, expand ln(x^3/y^1).
4
For x > 0 and y > 0, expand ln(x^2/y^4).
5
For x > 0 and y > 0, expand ln(x^5/y^3).
6
For x > 0 and y > 0, expand ln(x^3/y^2).
Answer Key
1. 2 ln(x) − 5 ln(y)2. 1 ln(x) − 4 ln(y)3. 3 ln(x) − 1 ln(y)4. 2 ln(x) − 4 ln(y)5. 5 ln(x) − 3 ln(y)6. 3 ln(x) − 2 ln(y)