12th Grade Logarithms and Exponential Equations Worksheet — Level 3 — Practice Set 3 — 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 3 — 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 as a single logarithm: log 56 − log 7
Answer: log 8
log a − log b = log (a ÷ b)
2.Solve: 2x + 5 = 4
Answer: x = −3
- 4 = 22
- x + 5 = 2
- x = −3
3.Evaluate log₂ 16.
Answer: 4
24 = 16
4.Write as a single logarithm: log 8 + log 6
Answer: log 48
log a + log b = log ab
5.Evaluate log₃ 1.
Answer: 0
30 = 1
6.Solve: 33x = 19683
Answer: x = 3
- 19683 = 39
- 3x = 9
- x = 3
7.Evaluate log₁₀ 10.
Answer: 1
101 = 10
8.Write as a single logarithm: log 30 − log 6
Answer: log 5
log a − log b = log (a ÷ b)
9.Solve: 2x − 2 = 2
Answer: x = 3
- 2 = 21
- x − 2 = 1
- x = 3
10.Evaluate log₁₀ 1000.
Answer: 3
103 = 1000
11.Evaluate log₂ 64.
Answer: 6
26 = 64
12.Evaluate log₁₀ 1.
Answer: 0
100 = 1
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.