Year 12 Logarithms and Exponential Equations Worksheet — Level 1 — Practice Set 4 — 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 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 32 = 9 in logarithm form.
Answer: log₃ 9 = 2
ax = y means logₐ y = x.
2.Write 53 = 125 in logarithm form.
Answer: log₅ 125 = 3
ax = y means logₐ y = x.
3.Write 21 = 2 in logarithm form.
Answer: log₂ 2 = 1
ax = y means logₐ y = x.
4.Evaluate log₁₀ 10.
Answer: 1
101 = 10
5.Write 52 = 25 in logarithm form.
Answer: log₅ 25 = 2
ax = y means logₐ y = x.
6.Write 51 = 5 in logarithm form.
Answer: log₅ 5 = 1
ax = y means logₐ y = x.
7.Evaluate log₂ 4.
Answer: 2
22 = 4
8.Write 101 = 10 in logarithm form.
Answer: log₁₀ 10 = 1
ax = y means logₐ y = x.
9.Write 104 = 10000 in logarithm form.
Answer: log₁₀ 10000 = 4
ax = y means logₐ y = x.
10.Evaluate log₅ 5.
Answer: 1
51 = 5
11.Evaluate log₅ 125.
Answer: 3
53 = 125
12.Write 33 = 27 in logarithm form.
Answer: log₃ 27 = 3
ax = y means logₐ y = x.
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.