Year 11 Logarithms and Exponential Equations Worksheet — Level 3 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 11 exponentials & logarithms worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Exponentials & LogarithmsYear 11 Logarithms and Exponential Equations Worksheet — Level 3 — Practice Set 3 — Answers
logₐ y = x means ax = y. Log laws: log a + log b = log ab; log a − log b = log (a ÷ b); log aⁿ = n log a.
1.Evaluate log₃ .
Answer: -1
3-1 =
2.Evaluate log₃ 3.
Answer: 1
31 = 3
3.Write as a single logarithm: log 30 − log 6
Answer: log 5
log a − log b = log (a ÷ b)
4.Evaluate log₂ 2.
Answer: 1
21 = 2
5.Solve: 22x + 2 = 4
Answer: x = 0
- 4 = 22
- 2x + 2 = 2
- x = 0
6.Evaluate log₃ 81.
Answer: 4
34 = 81
7.Write as a single logarithm: log 8 + log 4
Answer: log 32
log a + log b = log ab
8.Evaluate log₁₀ 1.
Answer: 0
100 = 1
9.Solve: 23x − 3 = 64
Answer: x = 3
- 64 = 26
- 3x − 3 = 6
- x = 3
10.Evaluate log₂ 16.
Answer: 4
24 = 16
11.Write as a single logarithm: log 28 − log 7
Answer: log 4
log a − log b = log (a ÷ b)
12.Evaluate log₅ 625.
Answer: 4
54 = 625
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
- For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
- Celebrate what went well first, then pick one thing to work on next.