Year 13 Logarithms and Exponential Equations Worksheet — Level 2 — Answers
Answer sheet with worked solutions for the Year 13 exponentials & logarithms worksheet.
Success TutoringWorksheetsAnswer sheetYear 13 · Mathematics · Exponentials & LogarithmsYear 13 Logarithms and Exponential Equations Worksheet — Level 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 25 = 32 in logarithm form.
Answer: log₂ 32 = 5
ax = y means logₐ y = x.
2.Write 27 = 128 in logarithm form.
Answer: log₂ 128 = 7
ax = y means logₐ y = x.
3.Evaluate log₁₀ .
Answer: -1
10-1 =
4.Write 53 = 125 in logarithm form.
Answer: log₅ 125 = 3
ax = y means logₐ y = x.
5.Write as a single logarithm: log 24 − log 6
Answer: log 4
log a − log b = log (a ÷ b)
6.Write 23 = 8 in logarithm form.
Answer: log₂ 8 = 3
ax = y means logₐ y = x.
7.Evaluate log₂ 64.
Answer: 6
26 = 64
8.Evaluate log₂ 1.
Answer: 0
20 = 1
9.Evaluate log₂ .
Answer: -2
2-2 =
10.Write as a single logarithm: log 8 + log 7
Answer: log 56
log a + log b = log ab
11.Evaluate log₂ 2.
Answer: 1
21 = 2
12.Write 20 = 1 in logarithm form.
Answer: log₂ 1 = 0
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.