# Topic Questions: • understand the definition and properties of $\mathrm{e}^x$ and $\ln x$, including their relationship as inverse functions and their graphs — 9709 P3 Logarithmic and exponential functions

> 9 9709 P3 Logarithmic and exponential functions topic questions (26 marks) on understand the definition and properties of … and… — 7 papers, 2020–2025. Open…

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CIE IAL · Mathematics · 9709 P3 · Logarithmic and exponential functions

9 9709 P3 Logarithmic and exponential functions topic questions are tagged to this syllabus point across 7 papers (2020–2025). Only the parts whose knowledge graph matches this syllabus statement are counted, and the table shows which parts of each question are involved.

- 9 topic questions
- 7 papers
- 26 tagged marks
- 13.2% of topic questions
- 10.6% of topic marks
- 2020–2025
- Syllabus 2020–2027
- [All 9709 P3 Logarithmic and exponential functions topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/logarithmic-and-exponential-functions/)
- [All paper codes](https://www.examsci.com/topics/)

Core finding

**This Logarithmic and exponential functions syllabus point appears in 7 9709 P3 papers across 2020–2025, contributing 9 topic questions and 26 marks.** The most recent appearance is 9709/32 March 2025. That equals 13.2% of the 68 topic questions and 10.6% of the 245 marks tagged to Logarithmic and exponential functions. Only parts tagged to this subtopic are counted, so a four-part question can contribute one item and one part's marks. The table lists every matching question, its tagged parts and marks, with a link back to the paper page. Sessions are newest first, so the statement can be traced back through the full paper history.

## Topic questions by session

Newest sessions first. Parts and marks count only the parts tagged to this subtopic; “x of y parts” shows how much of the question is tagged elsewhere. Select the paper cell to open the matching question on the paper page, or use **Go to Practice Hub** to answer that exact question in the Interactive Practice Hub.

| Paper | Question | Type | Parts | Marks | Difficulty | Practice |
| --- | --- | --- | --- | --- | --- | --- |
| [**9709/32** March 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-march-9709-32/#q-1) | **Q1** Solving Logarithmic Equation - CIE A-Level Math 2025 Mar Paper 32 Q1 | FRQ | 1 part | 3 | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=ebe23b18-f2b2-4e16-8e60-c5ac5649cb15&question_id=2e4e0d0b-8ded-4778-b491-6640e914f522&source_detail=9709%2F32+March+2025) |
| [**9709/31** October/November 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2024-october-november-9709-31/#q-3) | **Q3** Implicit Differentiation of Logarithmic Curve - CIE A-Level Maths 2024 Nov Paper 31 Q3 | FRQ | 1 part | 4 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=70a34762-5adb-4bbc-a073-ccdcbf562e7c&question_id=8b7a0650-f1e0-4264-9417-64c954ca5518&source_detail=9709%2F31+October%2FNovember+2024) |
| [**9709/31** October/November 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2024-october-november-9709-31/#q-5) | **Q5** Numerical Roots of Exponential and Logarithmic Equation - CIE A-Level Maths 2024 Nov Paper 31 Q5 | FRQ | 1 of 3 parts ((a)) | 2 of 7 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=70a34762-5adb-4bbc-a073-ccdcbf562e7c&question_id=d0b855b3-1cd8-4686-a7b8-cde45f5199d4&source_detail=9709%2F31+October%2FNovember+2024) |
| [**9709/33** October/November 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2024-october-november-9709-33/#q-3) | **Q3** Exponential Growth and Linearization - CIE A-Level Pure Mathematics 2024 Nov Q3 | FRQ | 1 of 2 parts ((a)) | 3 of 5 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=eea0ef07-a2e6-40ec-b1f1-0940ce02a199&question_id=2238760a-2c91-4ec1-a2e8-f7d6f1381e23&source_detail=9709%2F33+October%2FNovember+2024) |
| [**9709/32** March 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2023-march-9709-32/#q-1) | **Q1** Express y in terms of x - CIE Pure Mathematics 2023 Mar Paper 32 Q1 | FRQ | 1 part | 3 | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=fb85986e-2f5e-482c-8e08-173425b67cc3&question_id=346df59a-f107-4911-8e09-ff119e5e489c&source_detail=9709%2F32+March+2023) |
| [**9709/33** October/November 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2022-october-november-9709-33/#q-1) | **Q1** Logarithmic Equation - CIE Pure Mathematics 3 | FRQ | 1 part | 4 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=955ef535-8636-46dc-9b2a-f083375bbec1&question_id=aaa68729-6be0-4c3c-8314-ee044f9e50d5&source_detail=9709%2F33+October%2FNovember+2022) |
| [**9709/32** May/June 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2022-may-june-9709-32/#q-1) | **Q1** Solve Logarithmic Equation - CIE Mathematics 2022 Jun Q1 | FRQ | 1 part | 4 | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6ad396ce-ab9f-4c82-bba2-087b907a1ea1&question_id=ee313d0f-d537-4093-aeac-1dc8de971cdf&source_detail=9709%2F32+May%2FJune+2022) |
| [**9709/32** May/June 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2022-may-june-9709-32/#q-6) | **Q6** Separable Differential Equation - CIE Mathematics 2022 Jun Q6 | FRQ | 1 of 2 parts ((b)) | 1 of 8 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6ad396ce-ab9f-4c82-bba2-087b907a1ea1&question_id=e5fdf76f-f2e0-49fe-a85c-887146d005f4&source_detail=9709%2F32+May%2FJune+2022) |
| [**9709/33** May/June 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2020-may-june-9709-33/#q-3) | **Q3** Exponential Equation and Logarithms - CIE Pure Mathematics 2020 Jun Q3 | FRQ | 1 of 2 parts ((a)) | 2 of 6 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=ff5efdae-7baa-4c33-aa9c-f8b1c25c428d&question_id=05bd246b-2135-4ac8-91f6-b18f26a83fb9&source_detail=9709%2F33+May%2FJune+2020) |

## Related topic questions in Logarithmic and exponential functions

- [• understand the relationship between logarithms and indices, and use the laws of logarithms (excluding change of base)](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/logarithmic-and-exponential-functions/understand-the-relationship-between-logarithms-and-indices-and-use-the-laws-of/) — 23 question items · 22 papers — 88 marks · 2020–2026
- [• use logarithms to solve equations and inequalities in which the unknown appears in indices](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/logarithmic-and-exponential-functions/use-logarithms-to-solve-equations-and-inequalities-in-which-the-unknown-appears-in/) — 27 question items · 25 papers — 104 marks · 2020–2026
- [• use logarithms to transform a given relationship to linear form, and hence determine unknown constants by considering the gradient and/or intercept](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/logarithmic-and-exponential-functions/use-logarithms-to-transform-a-given-relationship-to-linear-form-and-hence-determine/) — 11 question items · 8 papers — 36 marks · 2021–2026

## Topic question rules and edge cases

**How many topic questions cover this syllabus point?**

9 question stems cover this subtopic across 7 papers, but only 9 tagged parts and 26 marks belong to it. Other parts of the same questions are assessed under different statements and are excluded from this page.

**Which papers include this subtopic?**

The table lists every matching session from 2020–2025. Each row links to the question anchor on the paper page, where the full paper context and practice entry point are available.

**Why can one question appear under several subtopics?**

The parts of one question can assess different syllabus statements. Each part is counted under its own subtopics, so the same question stem can appear on several subtopic pages while each page lists only the parts and marks tagged to that statement.

**Can I practise these questions with AI marking?**

Yes. Open a paper from the table and use the Interactive Practice Hub entry point. The page itself is static HTML so search engines and retrieval agents can read the full question list without executing JavaScript.

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Full page with native tables, bar charts and Practice Hub links: https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/logarithmic-and-exponential-functions/understand-the-definition-and-properties-of-mathrm-e-x-and-ln-x-including-their/