Year 11 Logarithms and Exponential Equations Worksheet — Level 2 — Practice Set 2 — 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 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.Write 33 = 27 in logarithm form.
Answer: log₃ 27 = 3
ax = y means logₐ y = x.
2.Write 22 = 4 in logarithm form.
Answer: log₂ 4 = 2
ax = y means logₐ y = x.
3.Evaluate log₅ 25.
Answer: 2
52 = 25
4.Write as a single logarithm: log 12 − log 4
Answer: log 3
log a − log b = log (a ÷ b)
5.Evaluate log₁₀ 100.
Answer: 2
102 = 100
6.Evaluate log₁₀ 10000.
Answer: 4
104 = 10000
7.Write as a single logarithm: log 32 − log 4
Answer: log 8
log a − log b = log (a ÷ b)
8.Write as a single logarithm: log 6 + log 3
Answer: log 18
log a + log b = log ab
9.Write 50 = 1 in logarithm form.
Answer: log₅ 1 = 0
ax = y means logₐ y = x.
10.Write 52 = 25 in logarithm form.
Answer: log₅ 25 = 2
ax = y means logₐ y = x.
11.Write 26 = 64 in logarithm form.
Answer: log₂ 64 = 6
ax = y means logₐ y = x.
12.Evaluate log₅ .
Answer: -1
5-1 =
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.