Year 10 Logarithms and Exponential Equations Worksheet — Level 3 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 10 exponentials & logarithms worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Exponentials & LogarithmsYear 10 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.Solve: 10x − 3 = 100
Answer: x = 5
- 100 = 102
- x − 3 = 2
- x = 5
2.Write as a single logarithm: log 8 + log 7
Answer: log 56
log a + log b = log ab
3.Write as a single logarithm: log 56 − log 7
Answer: log 8
log a − log b = log (a ÷ b)
4.Solve: 32x = 729
Answer: x = 3
- 729 = 36
- 2x = 6
- x = 3
5.Solve: 32x + 4 = 81
Answer: x = 0
- 81 = 34
- 2x + 4 = 4
- x = 0
6.Write as a single logarithm: log 2 + log 6
Answer: log 12
log a + log b = log ab
7.Evaluate log₅ 1.
Answer: 0
50 = 1
8.Solve: 3x − 2 = 9
Answer: x = 4
- 9 = 32
- x − 2 = 2
- x = 4
9.Write as a single logarithm: log 8 + log 6
Answer: log 48
log a + log b = log ab
10.Evaluate log₂ 32.
Answer: 5
25 = 32
11.Write as a single logarithm: log 7 + log 2
Answer: log 14
log a + log b = log ab
12.Write as a single logarithm: log 2 + log 7
Answer: log 14
log a + log b = log ab
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.