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This topic uses logarithms to turn exponential and power relationships into straight lines — plotting log y against x, or log y against log x — so unknown constants are found from the gradient and intercept. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive course teaches the method with worked examples and gives instant-feedback practice questions to lock it in.
How you do it
Take logs of both sides of the model to get something in the form Y equals mX plus c. The gradient and intercept of the straight line then give the constants. Which quantity to log depends on whether the model is a power law or exponential.
Before you start
The groundwork here is the laws of logarithms and straight lines. Keep it sharp for fitting models to data.
What you learn
We'll build both laws, read gradients and intercepts off real diagrams, and remember the step students most often miss — un-logging the intercept. Forgetting this is the single most common error. The course works through why taking logs straightens the curve, reading a graph or two data points and using the fitted model. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
We teach Logarithmic Graphs (Linear Form) as one of the Exponentials & Logarithms topics in our A-level course library, at the second year of A-level. You work through 5 concepts and 5 worked examples, testing yourself at 5 points. Nearby topics in the same strand are Natural Logarithms & e, Solving Equations Using Logarithms and Changing the Base. You can drill this strand further on the Exponentials & Logarithms revision engine, with your accuracy saved to your skill tree.
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