Year 12 Logarithms and Exponential Equations Worksheet — Level 1 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 12 exponentials & logarithms worksheet.
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · Exponentials & LogarithmsYear 12 Logarithms and Exponential Equations Worksheet — Level 1 — 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.Write 31 = 3 in logarithm form.
Answer: log₃ 3 = 1
ax = y means logₐ y = x.
2.Evaluate log₃ 9.
Answer: 2
32 = 9
3.Evaluate log₁₀ 100.
Answer: 2
102 = 100
4.Write 53 = 125 in logarithm form.
Answer: log₅ 125 = 3
ax = y means logₐ y = x.
5.Evaluate log₅ 25.
Answer: 2
52 = 25
6.Write 52 = 25 in logarithm form.
Answer: log₅ 25 = 2
ax = y means logₐ y = x.
7.Evaluate log₂ 32.
Answer: 5
25 = 32
8.Write 101 = 10 in logarithm form.
Answer: log₁₀ 10 = 1
ax = y means logₐ y = x.
9.Evaluate log₃ 27.
Answer: 3
33 = 27
10.Evaluate log₃ 3.
Answer: 1
31 = 3
11.Write 23 = 8 in logarithm form.
Answer: log₂ 8 = 3
ax = y means logₐ y = x.
12.Evaluate log₅ 625.
Answer: 4
54 = 625
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.