Find log₂(8).
- Ask which power of 2 gives 8.
- 2³ = 8.
Answer: 3
Logarithmic Functions Worksheets
Evaluate exponentials and logarithms using inverse relationships, with positive log arguments.
Learn the skill
Logarithms as exponents
For a positive base b other than 1, log_b(a) is the exponent to which b must be raised to produce a. In real-number logarithms, the argument a must be positive.
A method you can use
- Identify the base, argument, and unknown exponent.
- Translate log_b(a) = c into b raised to c equals a.
- Evaluate or solve, then check that every original logarithm has a positive argument.
Worked examples
Find log₁₀(0.01).
- 0.01 is 1/100.
- 10 raised to −2 equals 1/100.
Answer: −2
Solve log₃(x) = 4.
- Rewrite in exponential form: x = 3⁴.
- 81 is positive, so it is allowed.
Answer: x = 81
Try it yourself
Solve these before opening the answers. The printable sets below give you more practice.
1. Find log₂(32).
Show answer and explanation
5
2⁵ = 32.
2. Solve log₅(x) = 2.
Show answer and explanation
x = 25
Rewrite as x = 5²; 25 is positive.
Before you begin
Factor polynomials, use exponent laws and solve equations with domain restrictions.
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.
2
Evaluate log base 4 of 4.
3
Evaluate log base 5 of 125.
4
Evaluate log base 4 of 16.
5
Evaluate log base 4 of 1024.
6
Evaluate log base 5 of 3125.
Answer Key
1. 22. 13. 34. 25. 56. 5