Year 11 Logarithms and Exponential Equations Worksheet — Level 2 — 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 2 — 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.Write 54 = 625 in logarithm form.
Answer: log₅ 625 = 4
ax = y means logₐ y = x.
2.Evaluate log₃ 9.
Answer: 2
32 = 9
3.Write 33 = 27 in logarithm form.
Answer: log₃ 27 = 3
ax = y means logₐ y = x.
4.Write 22 = 4 in logarithm form.
Answer: log₂ 4 = 2
ax = y means logₐ y = x.
5.Write as a single logarithm: log 4 + log 5
Answer: log 20
log a + log b = log ab
6.Evaluate log₂ 2.
Answer: 1
21 = 2
7.Evaluate log₃ .
Answer: -2
3-2 =
8.Evaluate log₁₀ .
Answer: -2
10-2 =
9.Write as a single logarithm: log 40 − log 5
Answer: log 8
log a − log b = log (a ÷ b)
10.Write as a single logarithm: log 16 − log 4
Answer: log 4
log a − log b = log (a ÷ b)
11.Write 50 = 1 in logarithm form.
Answer: log₅ 1 = 0
ax = y means logₐ y = x.
12.Write as a single logarithm: log 54 − log 6
Answer: log 9
log a − log b = log (a ÷ b)
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.