Year 11 Logarithms and Exponential Equations Worksheet — Level 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 — 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 .
Answer: -2
2-2 =
2.Evaluate log₁₀ 10.
Answer: 1
101 = 10
3.Write as a single logarithm: log 9 + log 3
Answer: log 27
log a + log b = log ab
4.Write as a single logarithm: log 81 − log 9
Answer: log 9
log a − log b = log (a ÷ b)
5.Evaluate log₂ 32.
Answer: 5
25 = 32
6.Write as a single logarithm: log 32 − log 8
Answer: log 4
log a − log b = log (a ÷ b)
7.Solve: 10x − 3 = 1000
Answer: x = 6
- 1000 = 103
- x − 3 = 3
- x = 6
8.Write as a single logarithm: log 6 + log 2
Answer: log 12
log a + log b = log ab
9.Write as a single logarithm: log 56 − log 7
Answer: log 8
log a − log b = log (a ÷ b)
10.Solve: 102x + 2 = 100
Answer: x = 0
- 100 = 102
- 2x + 2 = 2
- x = 0
11.Evaluate log₅ 625.
Answer: 4
54 = 625
12.Evaluate log₁₀ 100.
Answer: 2
102 = 100
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.