IP AMaths Notes (Upper Sec, Year 3-4): 02) Logarithms and Exponentials
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Log laws, change of base, and exponential modelling with inverse relationships for IP Additional Mathematics.
Last updated 30 Nov 2025
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- Start Here
- 1 Core facts
- 2 Worked example - Solve logarithmic equation
- 3 Worked example - Linear law
Q: What does IP AMaths Notes (Upper Sec, Year 3-4): 02) Logarithms and Exponentials cover?
A: Log laws, change of base, and exponential modelling with inverse relationships for IP Additional Mathematics.
Logarithms invert exponentials. Switch comfortably between both forms to linearise growth models and solve equations involving powers.
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These notes align with SEAB GCE O-Level Additional Mathematics (4049) content used in IP programmes (exams from 2025).
Status: SEAB O-Level Additional Mathematics 4049 syllabus (exams from 2025) checked 2025-11-30 - scope unchanged; remains the reference for this note.
Start Here
| Read time | What to take away |
| 1 second | Logarithms undo exponentials. |
| 10 seconds | Before using log laws, check the domain: every logged expression must be positive. After solving, reject any root that breaks that condition. |
| 100 seconds | Example: if log(x + 3) + log(x - 1) appears, the domain is x greater than 1 before any quadratic solving starts. |
1 Core facts
- Definition:
