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WorksheetYear 12Level 3 · Challenge

Free 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 ready to stretch further. This Year 12 worksheet has 12 questions and comes with a full answer sheet showing the working for every question.

Need more practice? Practice Set 2 · 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
England National 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: England National 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

  1. 1Year 12 Arithmetic and Geometric Sequences Worksheet — Level 1
  2. 2Year 12 Arithmetic and Geometric Sequences Worksheet — Level 2
  3. 3Year 12 Arithmetic and Geometric Sequences Worksheet — Level 3
← Easier: Level 2 · Standard

How to use this worksheet

  1. Print the PDF or complete it on screen. Write the student's name and date at the top.
  2. Read the instructions for each part together before starting. Encourage working to be shown, not just answers.
  3. Mark with the answer sheet. Compare the method, not only the final answer, and give credit for correct working.
  4. 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 17–18) 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 & Logarithms

Year 12 Logarithms and Exponential Equations Worksheet — Level 3

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.Solve: 102x = 1000000
2.Write as a single logarithm: log 7 + log 3 (answer space)
3.Evaluate log₁₀ 1000. (answer space)
4.Solve: 22x − 2 = 4
5.Evaluate log₅ 1. (answer space)
6.Write as a single logarithm: log 2 + log 6 (answer space)
7.Write as a single logarithm: log 16 − log 4 (answer space)
8.Evaluate log₁₀ 10000. (answer space)
9.Evaluate log₁₀ 100. (answer space)
10.Evaluate log₅ 125. (answer space)
11.Write as a single logarithm: log 36 − log 9 (answer space)
12.Write as a single logarithm: log 12 − log 6 (answer space)
Free worksheets at worksheets.successtutoring.com · © Success Tutoring · Free for personal and classroom use

Preview — the PDF contains the full resource and answer sheet.

More Year 12 exponentials & logarithms resources

  • 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

Exponentials & Logarithms in other year levels

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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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