# 9709 P3 Logarithmic and exponential functions Topic Questions > CIE IAL 9709 P3: every Logarithmic and exponential functi… topic question from 48 papers (2020–2026), grouped by syllabus point. 68 questions, 245 marks,… - Canonical HTML: https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/logarithmic-and-exponential-functions/ - Markdown mirror: https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/logarithmic-and-exponential-functions/index.md --- CIE IAL · Mathematics · 9709 P3 · A Level Every 9709 P3 Logarithmic and exponential functions topic question from the 2020–2027 syllabus, drawn from 48 papers (2020–2026) and grouped by syllabus point. Each row opens a page listing the exact question numbers, marks and a direct link into the paper. These are questions by topic, not full papers, so you can revise one topic at a time. - 9709 P3 - 4 subtopics - 68 topic questions - 48 papers - 245 tagged marks - [Back to Logarithmic and exponential functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/logarithmic-and-exponential-functions/) - [All paper codes](https://www.examsci.com/topics/) Core finding **use logarithms to solve equations and inequalities in which the… is the most frequently assessed subtopic in Logarithmic and exponential functions, with 27 topic questions and 104 marks across 25 papers.** understand the relationship between logarithms and indices… follows with 23 topic questions and 88 marks. The topic contains 4 subtopics, 68 topic questions and 245 marks in total. Rows count only the parts tagged to that subtopic, keep the same colour in both charts and repeat paper count, tagged marks and year range in the native table. ## Topic question count and mark distribution Subtopics are on the vertical axis and sorted from highest to lowest. Only the parts whose knowledge graph matches a subtopic are counted for it, and percentages are each row's share of the tagged total in that chart. A part tagged to several subtopics is counted in each bar, so the bars are not a partition of the topic total. ### Questions by subtopic question items - [• 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/) (25 papers) — 27 · 38.6% - [• 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/) (22 papers) — 23 · 32.9% - [• 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/) (8 papers) — 11 · 15.7% - [• 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-p3/logarithmic-and-exponential-functions/understand-the-definition-and-properties-of-mathrm-e-x-and-ln-x-including-their/) (7 papers) — 9 · 12.9% ### Marks by subtopic marks - [• 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/) (25 papers) — 104 · 40.9% - [• 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/) (22 papers) — 88 · 34.6% - [• 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/) (8 papers) — 36 · 14.2% - [• 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-p3/logarithmic-and-exponential-functions/understand-the-definition-and-properties-of-mathrm-e-x-and-ln-x-including-their/) (7 papers) — 26 · 10.2% ## Subtopic comparison matrix Curriculum order is by syllabus number, then alphabetically. Every row links to the matching past-paper question list. | Subtopic | Topic questions | Papers | Marks | Years | | | --- | --- | --- | --- | --- | --- | | **[• 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-p3/logarithmic-and-exponential-functions/understand-the-definition-and-properties-of-mathrm-e-x-and-ln-x-including-their/)** | 9 | 7 | 26 | 2020–2025 | [Open topic questions](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/) | | **[• 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 | 22 | 88 | 2020–2026 | [Open topic questions](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/) | | **[• 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 | 25 | 104 | 2020–2026 | [Open topic questions](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/) | | **[• 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 | 8 | 36 | 2021–2026 | [Open topic questions](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/) | ## Browse every topic question - [• 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-p3/logarithmic-and-exponential-functions/understand-the-definition-and-properties-of-mathrm-e-x-and-ln-x-including-their/) — 9 question items · 7 papers — 26 marks · 2020–2025 - [• 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 ## Other topics in 9709 P3 - [Algebra 156 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/algebra/) - [Complex numbers 152 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/) - [Differential equations 75 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differential-equations/) - [Differentiation 134 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differentiation/) - [Integration 114 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/integration/) - [Numerical solution of equations 131 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/numerical-solution-of-equations/) - [Trigonometry 138 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/trigonometry/) - [Vectors 133 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/vectors/) ## Topic question rules and edge cases **How many subtopics does Logarithmic and exponential functions contain?** This page lists 4 subtopics tagged to the current syllabus. They are ordered by syllabus number, then alphabetically, and each row opens a page of matching past-paper questions. **How are the subtopic question and mark totals calculated?** A multiple-choice question contributes one item and its marks to every subtopic it is tagged with. A structured question contributes one item per tagged part, and that part’s marks; untagged parts of the same question are not counted here. A part tagged to several subtopics therefore appears under each of them. **Why do some subtopics have no numbered prefix?** Practical-skills statements and some syllabus bullets are unnumbered. Numbered statements come first; unnumbered statements and ties are sorted alphabetically. **Is the LaTeX rendered without JavaScript?** Yes. Subtopics that contain formulas are converted to static KaTeX HTML during the build, and the KaTeX stylesheet is served from the same site. --- 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/