# Topic Questions: • understand the relationship between logarithms and indices, and use the laws of logarithms (excluding change of base) — 9709 P2 Logarithmic and exponential functions > 31 9709 P2 Logarithmic and exponential functions topic questions (117 marks) on understand the relationship between logarithms… — 24 papers, 2020–2026. Open… - Canonical HTML: https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/logarithmic-and-exponential-functions/understand-the-relationship-between-logarithms-and-indices-and-use-the-laws-of/ - Markdown mirror: https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/logarithmic-and-exponential-functions/understand-the-relationship-between-logarithms-and-indices-and-use-the-laws-of/index.md --- CIE IAL · Mathematics · 9709 P2 · Logarithmic and exponential functions 31 9709 P2 Logarithmic and exponential functions topic questions are tagged to this syllabus point across 24 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. - 31 topic questions - 24 papers - 117 tagged marks - 24.8% of topic questions - 27.0% 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 24 9709 P2 papers across 2020–2026, contributing 31 topic questions and 117 marks.** The most recent appearance is 9709/21 May/June 2026. That equals 24.8% of the 125 topic questions and 27.0% 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 | | --- | --- | --- | --- | --- | --- | --- | | [**9709/21** May/June 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2026-may-june-9709-21/#q-1) | **Q1** Logarithmic Linear Transformation - CIE A Level Maths 2026 Jun Paper 21 Q1 | FRQ | 1 part | 4 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=be6f9351-4b56-44f4-a190-4c173afbab5c&question_id=fe25183f-6bf6-4d72-9372-1ac74631218c&source_detail=9709%2F21+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-3) | **Q3** Linear Model of Exponential Relationship - CIE 9709 Pure Mathematics 2026 Jun Paper 25 Q3 | FRQ | 1 part | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=676df908-86e2-4c2a-80d5-ab947b294392&question_id=75e47846-1f7d-444e-8065-3dd1ea96a2eb&source_detail=9709%2F25+May%2FJune+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-1) | **Q1** Logarithmic Equation with Exact Solution - CIE Pure Mathematics 2025 Paper 22 Q1 | FRQ | 1 part | 4 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=94e39d6f-4578-4f72-b7e3-69893082ab12&question_id=0ba3c07d-ea40-4ddf-bea7-1318ea0ef32a&source_detail=9709%2F22+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-6) | **Q6** Parametric Differentiation of Rational and Logarithmic Functions - CIE A-Level Maths 2025 Jun Paper 21 Q6 | FRQ | 1 of 3 parts ((b)) | 4 of 10 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=7cc2750a-19aa-484e-8c4b-2aed1e280b7f&question_id=75fdf0b4-3d87-49ce-8cae-c302e1f8a6a4&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-1) | **Q1** Integration of Rational Function - CIE Pure Mathematics 2025 Jun Paper 23 Q1 | FRQ | 1 part | 3 | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=af305940-211b-4b41-80d5-3d9e354abe46&question_id=05eddf67-3515-4265-95d8-bb8ff83badfc&source_detail=9709%2F23+May%2FJune+2025) | | [**9709/25** May/June 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2025-may-june-9709-25/#q-1) | **Q1** Definite Integral of Rational Function - CIE Pure Maths 2025 Jun P25 Q1 | FRQ | 1 part | 3 | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=466aeb86-ac3e-43be-be29-b0ae625577fb&question_id=62c5806a-2ee1-49e8-9630-8a2a65d42657&source_detail=9709%2F25+May%2FJune+2025) | | [**9709/25** May/June 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2025-may-june-9709-25/#q-4) | **Q4** Intersection of Exponential and Sine Curves - CIE Pure Maths 2025 Jun P25 Q4 | FRQ | 1 of 3 parts ((a)) | 1 of 8 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=466aeb86-ac3e-43be-be29-b0ae625577fb&question_id=da7a839b-ee8e-4aee-8592-f04c31c10104&source_detail=9709%2F25+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** 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) | | [**9709/22** October/November 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2024-october-november-9709-22/#q-4) | **Q4** Exponential and Modulus Graphs - CIE Pure Maths 2024 Nov Paper 22 Q4 | FRQ | 1 of 3 parts ((b)) | 2 of 7 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0904e585-d89a-413e-b330-5ca7eecd992d&question_id=be2bba87-aab0-4db2-85b2-0ebc6dc60229&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-7) | **Q7** Polynomial Division and Integration with Logarithms - CIE 9709 2024 Jun Paper 21 Q7 | FRQ | 1 of 2 parts ((b)) | 6 of 9 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=3464c125-e85d-44d4-bdd2-32e4a5934b26&question_id=3e7af132-4f54-4c87-b539-a4e1758f773c&source_detail=9709%2F21+May%2FJune+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-3) | **Q3** Definite Integration with Logarithmic and Exponential Functions - A-Level Mathematics | FRQ | 1 of 2 parts ((a)) | 4 of 6 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2f0de02e-594e-4f59-ab2b-49d765a478c4&question_id=c5369907-1621-43f4-816d-934c1908dc8b&source_detail=9709%2F21+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-3) | **Q3** Definite Integration of Rational and Exponential Functions - CIE P2 Q3 | FRQ | 1 of 2 parts ((a)) | 4 of 6 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6960ef2a-4ff5-4f3d-9627-9be49c72cf4e&question_id=466b3718-3ba4-45d1-916a-c6bf9e4f7139&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** May/June 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2023-may-june-9709-22/#q-3) | **Q3** Shaded Area Under Curve and Line - CIE Pure Mathematics 2023 May Paper 22 Q3 | FRQ | 1 part | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=12fd4d52-c299-46db-b59b-e6e1de7b4ef4&question_id=263c501c-9bb9-45c3-84bb-7a5e9d5e4643&source_detail=9709%2F22+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-5) | **Q5** Logarithmic Integration and Iterative Formula - CIE Pure Maths 2 2023 Mar Paper 22 Q5 | FRQ | 1 of 2 parts ((a)) | 5 of 8 on the paper | Hard | [Go to Practice Hub](https://www.examsci.com/practice?set_id=b4382735-9fe1-4e8c-abd7-e655c2a7e551&question_id=a4557df0-1ebf-462d-9e27-30a64d2982a2&source_detail=9709%2F22+March+2023) | | [**9709/21** May/June 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2022-may-june-9709-21/#q-1) | **Q1** Exponential Equation Linear Graph - CIE A Level Mathematics 2022 May Paper 21 Q1 | FRQ | 2 parts ((a), (b)) | 4 | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=12a191ee-c681-4394-a61e-8c35dee03851&question_id=db8144f7-807d-46b7-90bb-ef5a337894e9&source_detail=9709%2F21+May%2FJune+2022) | | [**9709/21** May/June 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2022-may-june-9709-21/#q-7) | **Q7** Polynomial Division and Definite Integral - CIE A Level Mathematics 2022 May Paper 21 Q7 | FRQ | 1 of 2 parts ((b)) | 6 of 9 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=12a191ee-c681-4394-a61e-8c35dee03851&question_id=8539482e-18e7-4b07-967b-f21be9b38dab&source_detail=9709%2F21+May%2FJune+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-4) | **Q4** Trapezium Rule with Logarithms - CIE P2 2022 Jun Q4 | FRQ | 1 of 2 parts ((a)) | 4 of 6 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=11942891-33a9-4c3a-b252-567ad1ff81c6&question_id=e5c21905-2dc3-4b7a-8bf4-a695cc5b7a16&source_detail=9709%2F23+May%2FJune+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-6) | **Q6** Area Under Exponential Curve Iteration - CIE P2 2022 Jun Q6 | FRQ | 1 of 2 parts ((a)) | 5 of 8 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=11942891-33a9-4c3a-b252-567ad1ff81c6&question_id=5f659a9c-77f3-43b3-8fd2-fd384313ce28&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-7) | **Q7** Implicit Differentiation and Numerical Iteration - CIE A-Level Mathematics Q7 | FRQ | 1 of 4 parts ((c)) | 4 of 12 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=9f37a63e-4459-4d3f-ac95-87a61d538eab&question_id=c2bb06cc-71cf-4edf-9aa7-e9b837a4b6f1&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-4) | **Q4** Parametric Differentiation and Logarithms - CIE 9709 P21 2021 Jun Q4 | FRQ | 1 of 2 parts ((a)) | 3 of 8 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=494b1fa8-6a0d-40e7-b32e-99e138b84ea7&question_id=81130761-26b0-47c1-9bfa-12eaf54d27ef&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-1) | **Q1** Logarithmic Equation with Cotangent - CIE Math 2021 Jun Paper 22 Q1 | FRQ | 2 parts ((a), (b)) | 5 | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2646d336-680b-4771-b6c2-3441e98dce59&question_id=7018832f-a31f-41db-adbe-2f2c425d4302&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-5) | **Q5** Logarithmic Equation and Numerical Root Finding - CIE 9709 March 2021 Paper 22 Q5 | FRQ | 1 of 3 parts ((a)) | 3 of 8 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=4d0e0d7f-cb0d-4693-814b-b44deac42ee4&question_id=6c0a8797-4567-43f4-8cde-0721e03ecdb0&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) | | [**9709/22** 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-1) | **Q1** Logarithmic Equation - CIE 9709 2020 Jun Paper 21 Q1 | FRQ | 1 part | 3 | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=fcbdbf1b-c521-4d93-a486-3d0ce52ffd32&question_id=ce281a60-2685-4884-855f-3404a58da715&source_detail=9709%2F21+May%2FJune+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 ((b)) | 5 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-3) | **Q3** Definite Integral with Logarithms - CIE 9709 March 2020 Paper 22 Q3 | FRQ | 1 part | 6 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=f57b9f35-0404-4541-bb00-922d1c2aa857&question_id=1d95d049-e538-4c87-8ea0-61d9398c9d2f&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 - [• use logarithms to solve equations and inequalities in which the unknown appears in indices](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/logarithmic-and-exponential-functions/use-logarithms-to-solve-equations-and-inequalities-in-which-the-unknown-appears-in/) — 35 question items · 30 papers — 99 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-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?** 29 question stems cover this subtopic across 24 papers, but only 31 tagged parts and 117 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. **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. --- Full page with native tables, bar charts and Practice Hub links: https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/logarithmic-and-exponential-functions/understand-the-relationship-between-logarithms-and-indices-and-use-the-laws-of/