Year 12 Logarithms and Exponential Equations Worksheet — Level 1 — Practice Set 2 — 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 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 54 = 625 in logarithm form.
Answer: log₅ 625 = 4
ax = y means logₐ y = x.
2.Evaluate log₃ 81.
Answer: 4
34 = 81
3.Write 33 = 27 in logarithm form.
Answer: log₃ 27 = 3
ax = y means logₐ y = x.
4.Evaluate log₅ 625.
Answer: 4
54 = 625
5.Write 53 = 125 in logarithm form.
Answer: log₅ 125 = 3
ax = y means logₐ y = x.
6.Write 34 = 81 in logarithm form.
Answer: log₃ 81 = 4
ax = y means logₐ y = x.
7.Write 31 = 3 in logarithm form.
Answer: log₃ 3 = 1
ax = y means logₐ y = x.
8.Evaluate log₂ 64.
Answer: 6
26 = 64
9.Write 104 = 10000 in logarithm form.
Answer: log₁₀ 10000 = 4
ax = y means logₐ y = x.
10.Evaluate log₂ 2.
Answer: 1
21 = 2
11.Evaluate log₃ 3.
Answer: 1
31 = 3
12.Evaluate log₅ 5.
Answer: 1
51 = 5
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.