Year 11 Logarithms and Exponential Equations Worksheet — Level 3 — Practice Set 4 — 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 4 — 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 log₂ 8.
Answer: 3
23 = 8
2.Evaluate log₅ .
Answer: -2
5-2 =
3.Write as a single logarithm: log 4 + log 5
Answer: log 20
log a + log b = log ab
4.Solve: 23x = 64
Answer: x = 2
- 64 = 26
- 3x = 6
- x = 2
5.Evaluate log₁₀ .
Answer: -1
10-1 =
6.Evaluate log₂ 128.
Answer: 7
27 = 128
7.Write as a single logarithm: log 25 − log 5
Answer: log 5
log a − log b = log (a ÷ b)
8.Write as a single logarithm: log 8 + log 4
Answer: log 32
log a + log b = log ab
9.Evaluate log₂ 4.
Answer: 2
22 = 4
10.Write as a single logarithm: log 18 − log 9
Answer: log 2
log a − log b = log (a ÷ b)
11.Evaluate log₁₀ 1.
Answer: 0
100 = 1
12.Evaluate log₅ 1.
Answer: 0
50 = 1
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.