12th Grade Logarithms and Exponential Equations Worksheet — Level 2 — Practice Set 2 — Answers
Answer sheet with worked solutions for the 12th Grade exponentials & logarithms worksheet.
Success TutoringWorksheetsAnswer sheet12th Grade · Mathematics · Exponentials & Logarithms12th Grade 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 34 = 81 in logarithm form.
Answer: log₃ 81 = 4
ax = y means logₐ y = x.
2.Write 3-1 = in logarithm form.
Answer: log₃ = -1
ax = y means logₐ y = x.
3.Evaluate log₃ 27.
Answer: 3
33 = 27
4.Write as a single logarithm: log 56 − log 8
Answer: log 7
log a − log b = log (a ÷ b)
5.Write as a single logarithm: log 25 − log 5
Answer: log 5
log a − log b = log (a ÷ b)
6.Write 54 = 625 in logarithm form.
Answer: log₅ 625 = 4
ax = y means logₐ y = x.
7.Write 102 = 100 in logarithm form.
Answer: log₁₀ 100 = 2
ax = y means logₐ y = x.
8.Evaluate log₅ 5.
Answer: 1
51 = 5
9.Write as a single logarithm: log 3 + log 6
Answer: log 18
log a + log b = log ab
10.Write as a single logarithm: log 45 − log 5
Answer: log 9
log a − log b = log (a ÷ b)
11.Write as a single logarithm: log 24 − log 8
Answer: log 3
log a − log b = log (a ÷ b)
12.Write as a single logarithm: log 3 + log 4
Answer: log 12
log a + log b = log ab
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.