IP AMaths Notes (Upper Sec, Year 3-4): 02) Logarithms and Exponentials
Log laws, change of base, and exponential modelling with inverse relationships for IP Additional Mathematics.
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.
Keep the full topic roadmap handy via our IP Maths tuition hub so you can jump into related drills, quizzes, or diagnostics as you move through these notes.
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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.
The core idea is simple: Logarithms undo exponentials.
Use it as a working check: Before using log laws, check the domain: every logged expression must be positive. After solving, reject any root that breaks that condition.
Then go one layer deeper: Example: if log(x + 3) + log(x - 1) appears, the domain is x greater than 1 before any quadratic solving starts.
Choosing the first transformation
Logarithm questions usually become short once you choose the right form. Start by identifying what needs to be isolated or straightened.
| Question cue | First transformation | Check before accepting the answer |
| Several logs with the same base are added or subtracted | Combine them into one log using product or quotient laws. | Every original logged expression must be positive, not just the combined expression. |
| A log equals a number | Convert to index form. |
