# Topic Questions: • use logarithms to solve equations and inequalities in which the unknown appears in indices — 9709 P2 Logarithmic and exponential functions

> 35 9709 P2 Logarithmic and exponential functions topic questions (99 marks) on use logarithms to solve equations and… — 30 papers, 2020–2026. Open the exact…

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CIE IAL · Mathematics · 9709 P2 · Logarithmic and exponential functions

35 9709 P2 Logarithmic and exponential functions topic questions are tagged to this syllabus point across 30 papers (2020–2026). Only the parts whose knowledge graph matches this syllabus statement are counted, and the table shows which parts of each question are involved.

- 35 topic questions
- 30 papers
- 99 tagged marks
- 28.0% of topic questions
- 22.9% of topic marks
- 2020–2026
- Syllabus 2020–2027
- [All 9709 P2 Logarithmic and exponential functions topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/logarithmic-and-exponential-functions/)
- [All paper codes](https://www.examsci.com/topics/)

Core finding

**This Logarithmic and exponential functions syllabus point appears in 30 9709 P2 papers across 2020–2026, contributing 35 topic questions and 99 marks.** The most recent appearance is 9709/22 May/June 2026. That equals 28.0% of the 125 topic questions and 22.9% of the 433 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 |
| --- | --- | --- | --- | --- | --- | --- |
| [**9709/22** May/June 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2026-may-june-9709-22/#q-5) | **Q5** Modulus Inequality - CIE Pure Mathematics 2026 Jun Paper 22 Q5 | FRQ | 1 of 2 parts ((b)) | 3 of 7 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=b091fc8c-1fe4-4654-936b-9d85d855edcc&question_id=aba2d8d6-ef11-45a3-87f5-d6187306ee19&source_detail=9709%2F22+May%2FJune+2026) |
| [**9709/23** May/June 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2026-may-june-9709-23/#q-5) | **Q5** Solving Modulus and Logarithmic Inequalities - CIE Pure Mathematics 2026 Jun Paper 23 Q5 | FRQ | 1 of 2 parts ((b)) | 3 of 7 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=71967dfb-f245-4aa9-8687-a354bca203f4&question_id=a1e120b9-0017-4eff-9551-e18ff3c6d557&source_detail=9709%2F23+May%2FJune+2026) |
| [**9709/25** May/June 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2026-may-june-9709-25/#q-5) | **Q5** Modulus Inequality and Logarithmic Application - CIE 9709 Pure Mathematics 2026 Jun Paper 25 Q5 | FRQ | 1 of 2 parts ((b)) | 3 of 7 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=676df908-86e2-4c2a-80d5-ab947b294392&question_id=6026a92f-0ff9-4d0b-b27a-a352fab08bec&source_detail=9709%2F25+May%2FJune+2026) |
| [**9709/22** March 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2026-march-9709-22/#q-2) | **Q2** Modulus Equation and Exponential Substitution - CIE 9709 P22 2026 Q2 | FRQ | 1 of 3 parts ((c)) | 2 of 6 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=b409e69d-9e6f-4ba0-8cd6-579cf789e935&question_id=b02f880a-aa7d-4c88-a7da-eb6a06f6c9bc&source_detail=9709%2F22+March+2026) |
| [**9709/22** October/November 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2025-october-november-9709-22/#q-3) | **Q3** Modulus Inequality and Exponential Application - CIE Pure Mathematics 2025 Paper 22 Q3 | FRQ | 1 of 2 parts ((b)) | 3 of 7 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=94e39d6f-4578-4f72-b7e3-69893082ab12&question_id=919d6b38-b03c-460c-8b78-bd7995fdae57&source_detail=9709%2F22+October%2FNovember+2025) |
| [**9709/23** October/November 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2025-october-november-9709-23/#q-2) | **Q2** Exponential Quadratic Equation - CIE P2 2025 Q2 | FRQ | 1 part | 3 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2675658d-907a-4273-bfc6-3e2a56654ef3&question_id=a91e8a2c-49cc-4abf-8976-640cd5ec6df7&source_detail=9709%2F23+October%2FNovember+2025) |
| [**9709/23** October/November 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2025-october-november-9709-23/#q-5) | **Q5** Area Bounded by Exponential Curve and Line - CIE P2 2025 Q5 | FRQ | 1 of 2 parts ((a)) | 2 of 7 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2675658d-907a-4273-bfc6-3e2a56654ef3&question_id=8aecfd47-3f5d-45f1-8396-b19363a755cb&source_detail=9709%2F23+October%2FNovember+2025) |
| [**9709/25** October/November 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2025-october-november-9709-25/#q-2) | **Q2** Exponential Quadratic Equation - CIE 9709 Pure Mathematics 2025 Nov Paper 25 Q2 | FRQ | 1 part | 3 | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d8e07605-f00e-45fb-a2b1-de7bd8ea23b9&question_id=201657f4-3449-4b58-94b6-4cf1b3dbedcf&source_detail=9709%2F25+October%2FNovember+2025) |
| [**9709/21** May/June 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2025-may-june-9709-21/#q-2) | **Q2** Exponential and Absolute Value Inequalities - CIE A-Level Maths 2025 Jun Paper 21 Q2 | FRQ | 2 of 3 parts ((a), (c)) | 3 of 6 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=7cc2750a-19aa-484e-8c4b-2aed1e280b7f&question_id=141cc616-ff63-4650-8c35-779628c198e3&source_detail=9709%2F21+May%2FJune+2025) |
| [**9709/23** May/June 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2025-may-june-9709-23/#q-4) | **Q4** Intersection and Area under Exponential and Trigonometric Curves - CIE Pure Mathematics 2025 Jun Paper 23 Q4 | FRQ | 1 of 3 parts ((a)) | 1 of 8 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=af305940-211b-4b41-80d5-3d9e354abe46&question_id=2b1b8273-7c67-435c-bae7-64bb4d1e9584&source_detail=9709%2F23+May%2FJune+2025) |
| [**9709/22** March 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2025-march-9709-22/#q-1) | **Q1** Logarithmic Equation - CIE A-Level Maths 2025 Mar Paper 22 Q1 | FRQ | 1 part | 3 | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=b6a2a173-49dc-4e3a-bd53-8608ce39b5e0&question_id=1af1b7e2-b466-4c8c-804d-631a9929f6e1&source_detail=9709%2F22+March+2025) |
| [**9709/22** March 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2025-march-9709-22/#q-3) | **Q3** Intersection and Area of Exponential Curves - CIE A-Level Maths 2025 Mar Paper 22 Q3 | FRQ | 1 of 2 parts ((a)) | 2 of 5 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=b6a2a173-49dc-4e3a-bd53-8608ce39b5e0&question_id=bcbe3d0a-aa02-4b4b-a8ee-7c84fae19452&source_detail=9709%2F22+March+2025) |
| [**9709/22** October/November 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2024-october-november-9709-22/#q-1) | **Q1** Logarithmic Equation - CIE Pure Maths 2024 Nov Paper 22 Q1 | FRQ | 1 part | 3 | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0904e585-d89a-413e-b330-5ca7eecd992d&question_id=36c4ba1a-f8de-4562-b69c-c42b86827557&source_detail=9709%2F22+October%2FNovember+2024) |
| [**9709/21** May/June 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2024-may-june-9709-21/#q-3) | **Q3** Modulus Inequality with Exponential Function - CIE 9709 2024 Jun Paper 21 Q3 | FRQ | 1 of 3 parts ((c)) | 2 of 8 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=3464c125-e85d-44d4-bdd2-32e4a5934b26&question_id=c28863f1-c448-47bf-94d0-34ae8ea97c77&source_detail=9709%2F21+May%2FJune+2024) |
| [**9709/23** May/June 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2024-may-june-9709-23/#q-2) | **Q2** Exponential Equation with Logarithms - CIE Pure Mathematics 2024 Jun Paper 23 Q2 | FRQ | 1 part | 4 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=68e9e6a6-c5e7-435e-ae19-09955e66fea6&question_id=d2d70191-16c3-46d5-80ea-e0f2a9bfec93&source_detail=9709%2F23+May%2FJune+2024) |
| [**9709/22** March 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2024-march-9709-22/#q-1) | **Q1** Exponential Equation with Logarithms - CIE 9709 March 2024 Paper 22 Q1 | FRQ | 1 part | 4 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=4e19c59f-2ff8-4fea-8c60-c0d2231e34bf&question_id=409cc833-7396-47dd-8f37-6ced6f7bf6c9&source_detail=9709%2F22+March+2024) |
| [**9709/21** October/November 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2023-october-november-9709-21/#q-4) | **Q4** Modulus Equation and Exponential Substitution - A-Level Mathematics | FRQ | 1 of 3 parts ((c)) | 2 of 7 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2f0de02e-594e-4f59-ab2b-49d765a478c4&question_id=a9cf1654-b8f1-4f42-b002-ad116c2a2118&source_detail=9709%2F21+October%2FNovember+2023) |
| [**9709/22** October/November 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2023-october-november-9709-22/#q-4) | **Q4** Modulus and Exponential Inequalities - CIE 9709 W23 QP 22 Q4 | FRQ | 2 of 4 parts ((c), (d)) | 4 of 9 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=f312d1ca-209a-4ae9-9051-b3c87f11cd3d&question_id=335c538f-2621-410b-863d-b7ef345facd5&source_detail=9709%2F22+October%2FNovember+2023) |
| [**9709/23** October/November 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2023-october-november-9709-23/#q-4) | **Q4** Modulus Graphs and Exponential Absolute Value Equations - CIE P2 Q4 | FRQ | 1 of 3 parts ((c)) | 2 of 7 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6960ef2a-4ff5-4f3d-9627-9be49c72cf4e&question_id=133d4a99-f163-4b00-bc01-6471e1c8cc61&source_detail=9709%2F23+October%2FNovember+2023) |
| [**9709/21** May/June 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2023-may-june-9709-21/#q-1) | **Q1** Solving Exponential Equation - CIE A-Level Mathematics 2023 Jun Paper 21 Q1 | FRQ | 1 part | 4 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=c04aa92d-8253-4bc2-ae3b-9903b11f4ea7&question_id=e7ccd21b-05e4-41ed-ac13-caff477a74b5&source_detail=9709%2F21+May%2FJune+2023) |
| [**9709/22** March 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2023-march-9709-22/#q-4) | **Q4** Modulus Function Graphs and Inequalities - CIE Pure Maths 2 2023 Mar Paper 22 Q4 | FRQ | 1 of 3 parts ((c)) | 2 of 7 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=b4382735-9fe1-4e8c-abd7-e655c2a7e551&question_id=1eb7dde5-3984-46b4-8341-b14ef20f976e&source_detail=9709%2F22+March+2023) |
| [**9709/21** October/November 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2022-october-november-9709-21/#q-2) | **Q2** Exponential Equation with Logarithms - CIE Pure Mathematics 2022 Nov Paper 21 Q2 | FRQ | 1 part | 4 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=69adb289-4fff-4b6d-8661-80adee6ac499&question_id=ef53f3f7-2c38-4e45-b44a-91d3823abb96&source_detail=9709%2F21+October%2FNovember+2022) |
| [**9709/23** October/November 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2022-october-november-9709-23/#q-2) | **Q2** Solving Exponential Equation with Logarithms - CIE Pure Mathematics 2022 Nov Paper 23 Q2 | FRQ | 1 part | 4 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=63ddbc4e-2b11-4af4-9085-1e4f522561f1&question_id=70c9319b-ab90-434a-9315-ae568356f958&source_detail=9709%2F23+October%2FNovember+2022) |
| [**9709/23** May/June 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2022-may-june-9709-23/#q-5) | **Q5** Polynomial Factorisation and Exponential Equation - CIE P2 2022 Jun Q5 | FRQ | 1 of 2 parts ((b)) | 3 of 7 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=11942891-33a9-4c3a-b252-567ad1ff81c6&question_id=7b45d0b3-8a8b-4c45-88b5-9286f9891f4a&source_detail=9709%2F23+May%2FJune+2022) |
| [**9709/22** March 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2022-march-9709-22/#q-3) | **Q3** Logarithmic Linear Graph Transformation - CIE A-Level Mathematics Q3 | FRQ | 1 of 2 parts ((b)) | 2 of 5 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=9f37a63e-4459-4d3f-ac95-87a61d538eab&question_id=59ddeb5c-b62b-4b2c-b54c-ebee5cc1fa32&source_detail=9709%2F22+March+2022) |
| [**9709/21** May/June 2021 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2021-may-june-9709-21/#q-7) | **Q7** Polynomial Factorisation and Exponential Equation - CIE 9709 P21 2021 Jun Q7 | FRQ | 1 of 3 parts ((c)) | 4 of 9 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=494b1fa8-6a0d-40e7-b32e-99e138b84ea7&question_id=005628eb-62c0-4070-99d4-cf0f388d46e2&source_detail=9709%2F21+May%2FJune+2021) |
| [**9709/22** May/June 2021 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2021-may-june-9709-22/#q-5) | **Q5** Polynomial Division and Exponential Transformation - CIE Math 2021 Jun Paper 22 Q5 | FRQ | 1 of 3 parts ((c)) | 2 of 7 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2646d336-680b-4771-b6c2-3441e98dce59&question_id=3fe044e0-d4b3-4086-a972-c75322e2432c&source_detail=9709%2F22+May%2FJune+2021) |
| [**9709/22** March 2021 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2021-march-9709-22/#q-6) | **Q6** Factor and Remainder Theorems with Exponential Substitution - CIE 9709 March 2021 Paper 22 Q6 | FRQ | 1 of 2 parts ((b)) | 5 of 10 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=4d0e0d7f-cb0d-4693-814b-b44deac42ee4&question_id=aca00213-9a37-43b2-8d89-f6be38728581&source_detail=9709%2F22+March+2021) |
| [**9709/21** October/November 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2020-october-november-9709-21/#q-1) | **Q1** Solving Logarithmic Equation - CIE Pure Mathematics 2020 Nov Paper 21 Q1 | FRQ | 1 part | 4 | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=4898eed1-24a8-40de-bf43-8e9d5d44f2c0&question_id=808bc85a-3fc7-4349-a005-0146ac7bcf31&source_detail=9709%2F21+October%2FNovember+2020) |
| [**9709/21** October/November 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2020-october-november-9709-21/#q-4) | **Q4** Absolute Value Equations and Exponential Forms - CIE Pure Mathematics 2020 Nov Paper 21 Q4 | FRQ | 1 of 2 parts ((b)) | 2 of 5 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=4898eed1-24a8-40de-bf43-8e9d5d44f2c0&question_id=60912a17-2651-470e-8d28-f33e56af5e0b&source_detail=9709%2F21+October%2FNovember+2020) |
| [**9709/22** October/November 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2020-october-november-9709-22/#q-2) | **Q2** Solving Exponential and Logarithmic Equation - CIE A-Level Pure Mathematics 2020 Nov Paper 22 Q2 | FRQ | 1 part | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=c2cdcfa2-f21a-403c-b726-74c0d9aa9740&question_id=83ab3c96-ff84-4e9f-bac7-1d8fd288d07f&source_detail=9709%2F22+October%2FNovember+2020) |
| [**9709/21** May/June 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2020-may-june-9709-21/#q-7) | **Q7** Polynomial Division and Integration - CIE 9709 2020 Jun Paper 21 Q7 | FRQ | 1 of 3 parts ((c)) | 4 of 12 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=fcbdbf1b-c521-4d93-a486-3d0ce52ffd32&question_id=46c59273-fa46-485f-a57b-eb3c56131dab&source_detail=9709%2F21+May%2FJune+2020) |
| [**9709/22** March 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2020-march-9709-22/#q-5) | **Q5** Modulus Function Graphs and Inequality - CIE 9709 March 2020 Paper 22 Q5 | FRQ | 1 of 3 parts ((c)) | 2 of 9 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=f57b9f35-0404-4541-bb00-922d1c2aa857&question_id=bd0d619d-c5b0-4173-aa58-7565983015ca&source_detail=9709%2F22+March+2020) |

## Related topic questions in Logarithmic and exponential functions

- [• understand the definition and properties of $\mathrm{e}^x$ and $\ln x$, including their relationship as inverse functions and their graphs](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/logarithmic-and-exponential-functions/understand-the-definition-and-properties-of-mathrm-e-x-and-ln-x-including-their/) — 32 question items · 24 papers — 123 marks · 2020–2026
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- [• 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-p2/logarithmic-and-exponential-functions/use-logarithms-to-transform-a-given-relationship-to-linear-form-and-hence-determine/) — 15 question items · 12 papers — 56 marks · 2021–2026

## Topic question rules and edge cases

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

33 question stems cover this subtopic across 30 papers, but only 35 tagged parts and 99 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 2020–2026. Each row links to the question anchor on the paper page, where the full paper context and practice entry point are available.

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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.

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