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This topic covers the natural logarithm ln x (log to base e) and its inverse eˣ, their graphs and key properties, and using ln to solve equations involving e. 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
The natural logarithm is log base e, and it undoes e to the power x exactly. Take ln of both sides to bring an exponent down. Keep answers in terms of e and ln where the question asks for an exact value.
Before you start
Get logarithms and exponential functions straight before you begin. It leads on to calculus with exponentials. It belongs to the Pure 3 specification.
What you learn
Pure 3 works with shifted and stretched versions. A negative root contributes nothing — discard it. 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
Natural Logarithms & e is a Exponentials & Logarithms topic in the A-level syllabus, covered here at the second year of A-level. The course is built from 5 concept sections, 5 worked examples and 5 check points before the exam-style set. Related topics students usually take next include Solving Equations Using Logarithms, Changing the Base and Exponential Functions & Graphs. For unlimited practice, the Exponentials & Logarithms revision engine builds new questions on demand and records your accuracy.
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