Study Guide
Index and Logarithm Laws
A senior study guide that sets out the index laws, the definition of a logarithm and the logarithm laws side by side. Worked examples…
- Difficulty
- Level 2 · Standard
- Time
- 25 min
Extra practice for Year 12 Logarithms and Exponential Equations Worksheet — Level 3: the same skill with fresh questions.
WorksheetYear 12Level 3 · Challenge
Free Year 12 Logarithms and Exponential Equations Worksheet — Level 3 — Practice Set 2
Practice Set 2 for Year 12 Logarithms and Exponential Equations Worksheet — Level 3: the same skill and level with a fresh set of questions and a full answer sheet.
More practice: Set 1 · Practice Set 3 · Practice Set 4 — same skill, fresh questions, full answers.
Instant download · No sign-up · Free for personal, classroom and homeschool use
- Year
- Year 12
- Subject
- Maths
- Topic
- Exponentials & Logarithms
- Difficulty
- Level 3 · Challenge
- Estimated time
- 15 minutes
- Curriculum
- New Zealand Curriculum
- Questions
- 12
- Answers
- Included, with working
- Format
- PDF (A4), print or complete online
Students will practise
- converting between index and logarithm form
- evaluating logarithms
- solving exponential equations
Curriculum: New Zealand Curriculum. We show specific outcome codes only where they have been verified against the official curriculum document.
What's next?
Completed: Year 12 Logarithms and Exponential Equations Worksheet — Level 3 — Practice Set 2
How to use this worksheet
- Print the PDF or complete it on screen. Write the student's name and date at the top.
- Read the instructions for each part together before starting. Encourage working to be shown, not just answers.
- Mark with the answer sheet. Compare the method, not only the final answer, and give credit for correct working.
- Record the score, celebrate what went well, then follow the "What's next" suggestion.
Common questions
Who is this worksheet for?
Year 12 students (typically ages 16–17) working on exponentials & logarithms. It is pitched at level 3 · challenge; an easier version is linked above.
Are the answers included?
Yes. The PDF includes a full answer sheet with the working for every question. You can also view the answers online.
How long does it take?
About 15 minutes for 12 questions. Short, regular sessions work best: two or three a week beats one long one.
Do I need to sign up to download?
No. Click Download Free PDF and it opens immediately. It is free for personal, classroom and homeschool use.
What should we do next?
Try Year 12 Arithmetic and Geometric Sequences Worksheet — Level 1.
Preview
Success TutoringWorksheetsYear 12 · Mathematics · Exponentials & LogarithmsYear 12 Logarithms and Exponential Equations Worksheet — Level 3 — Practice Set 2
Name
Date
Score /
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.Evaluate log₁₀ 1. (answer space)
2.Write as a single logarithm: log 2 + log 9 (answer space)
3.Solve: 103x + 6 = 1000
4.Write as a single logarithm: log 4 − log 2 (answer space)
5.Write as a single logarithm: log 6 − log 3 (answer space)
6.Write as a single logarithm: log 9 + log 2 (answer space)
7.Solve: 53x + 6 = 15625
8.Evaluate log₅ 625. (answer space)
9.Evaluate log₃ 3. (answer space)
10.Solve: 32x − 2 = 729
11.Evaluate log₅ 5. (answer space)
12.Evaluate log₅ 25. (answer space)
Preview — the PDF contains the full resource and answer sheet.
More Year 12 exponentials & logarithms resources
- Worksheet
Exponential Functions: Graphs, Equations and Models
A senior maths worksheet on exponential functions: features of the graphs of y = bˣ and their transformations (intercepts, asymptotes,…
- Difficulty
- Level 2 · Standard
- Time
- 50 min
- Questions
- 17 questions
- Answers
- Answers included
- Worksheet
Year 12 Logarithms and Exponential Equations Worksheet — Level 1
Convert between index and log form, evaluate logarithms, use the log laws and solve exponential equations. Builds confidence with the core…
- Difficulty
- Level 1 · Easier
- Time
- 15 min
- Questions
- 12 questions
- Answers
- Answers included
- Worksheet
Year 12 Logarithms and Exponential Equations Worksheet — Level 2
Convert between index and log form, evaluate logarithms, use the log laws and solve exponential equations. Expected-level practice for…
- Difficulty
- Level 2 · Standard
- Time
- 15 min
- Questions
- 12 questions
- Answers
- Answers included
- Worksheet
Year 12 Logarithms and Exponential Equations Worksheet — Level 3
Convert between index and log form, evaluate logarithms, use the log laws and solve exponential equations. A challenge set for students…
- Difficulty
- Level 3 · Challenge
- Time
- 15 min
- Questions
- 12 questions
- Answers
- Answers included
Exponentials & Logarithms in other year levels
- Year 11 Logarithms and Exponential Equations Worksheet — Level 1
Worksheet · Year 11 · Exponentials & Logarithms · Level 1 · Easier
- Year 11 Logarithms and Exponential Equations Worksheet — Level 2
Worksheet · Year 11 · Exponentials & Logarithms · Level 2 · Standard
- Year 13 Logarithms and Exponential Equations Worksheet — Level 1
Worksheet · Year 13 · Exponentials & Logarithms · Level 1 · Easier
- Year 13 Logarithms and Exponential Equations Worksheet — Level 2
Worksheet · Year 13 · Exponentials & Logarithms · Level 2 · Standard
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About this resource
- Created by
- Success Tutoring Maths Team
- Reviewed by
- Success Tutoring
- Last reviewed
- 1 October 2026
- How it was made
- Generated by checked procedures
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