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Logarithms are the inverse of exponentials: log_a b = c means aᶜ = b. This topic introduces logarithmic notation, evaluates simple logs and shows the relationship between exponential and logarithmic form. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive eClassroom course walks through each step with worked examples and instant-feedback questions, so you can practise until it's secure.
How you do it
A logarithm answers the question what power gives this number. Log base a of b equals c means a to the power c equals b. Converting between the two forms is the whole of the topic at this stage.
Before you start
The prerequisite is index laws. Pure 2 is where it is assessed. From here the path runs to the laws of logs and solving equations.
What you learn
We'll evaluate logs, switch fluently between power form and log form, meet the special values, use base-10 logs, and finish by seeing the log graph as the mirror image of the exponential graph. The base stays the base; the power and the answer swap roles. The course works through A logarithm is the inverse of a power, two ways to write the same fact, special values and the domain and base 10 — the common logarithm. 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 Introducing Logarithms as one of the Exponentials & Logarithms topics in our A-level course library, at the AS year. There are 5 teaching sections and 5 fully worked examples, plus 5 sets of check questions. Nearby topics in the same strand are Laws of Logarithms, Logarithmic Graphs (Linear Form), Natural Logarithms & e, Solving Equations Using Logarithms and Changing the Base. Endless extra practice on this strand is available on the Exponentials & Logarithms revision engine, which generates a fresh question each time.
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