Year 13 Logarithms and Exponential Equations Worksheet — Level 3 — Practice Set 2 — Answers
Answer sheet with worked solutions for the Year 13 exponentials & logarithms worksheet.
Success TutoringWorksheetsAnswer sheetYear 13 · Mathematics · Exponentials & LogarithmsYear 13 Logarithms and Exponential Equations Worksheet — Level 3 — Practice Set 2 — 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 log₁₀ .
Answer: -2
10-2 =
2.Write as a single logarithm: log 10 − log 2
Answer: log 5
log a − log b = log (a ÷ b)
3.Evaluate log₂ .
Answer: -1
2-1 =
4.Solve: 103x + 3 = 1000000
Answer: x = 1
- 1000000 = 106
- 3x + 3 = 6
- x = 1
5.Evaluate log₃ 27.
Answer: 3
33 = 27
6.Write as a single logarithm: log 5 + log 3
Answer: log 15
log a + log b = log ab
7.Evaluate log₂ 16.
Answer: 4
24 = 16
8.Write as a single logarithm: log 4 + log 8
Answer: log 32
log a + log b = log ab
9.Write as a single logarithm: log 7 + log 5
Answer: log 35
log a + log b = log ab
10.Write as a single logarithm: log 72 − log 9
Answer: log 8
log a − log b = log (a ÷ b)
11.Evaluate log₅ 1.
Answer: 0
50 = 1
12.Solve: 10x − 2 = 10
Answer: x = 3
- 10 = 101
- x − 2 = 1
- x = 3
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.