A-Level Mathematics Revision — Exponentials & Logarithms
Revise Exponentials & Logarithms for A-Level Mathematics with a topic explanation, worked example and common mistakes. Check the board notes for specification differences.
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- Exponentials & Logarithms in A-Level Mathematics: explanation, examples, and practice links on this page.
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What is Exponentials & Logarithms?
Exponentials and logarithms at A-Level explore the relationship between exponential growth/decay and their inverse functions, logarithms. You will learn the laws of logarithms, solve equations involving e and ln, and apply these concepts to model real-world phenomena like population growth or radioactive decay.
Board notes: All A-Level Maths boards (AQA, Edexcel, OCR) cover exponentials and logarithms in a similar way. The applications and modelling questions may differ slightly in context, but the core mathematical principles are the same.
Step-by-step explanationWorked examples
Worked example
Solve the equation e^(2x+1) = 5. Take the natural logarithm of both sides: ln(e^(2x+1)) = ln(5). This gives 2x+1 = ln(5). Rearranging for x, we get 2x = ln(5) - 1, so x = (ln(5) - 1)/2.
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Common mistakes
- 1Confusing the base of the logarithm. Remember that log(x) usually implies base 10, while ln(x) is the natural logarithm with base e.
- 2Incorrectly applying the laws of logarithms, such as log(a) + log(b) = log(ab) and log(a) - log(b) = log(a/b).
- 3Making errors when solving exponential equations. It's often necessary to take logarithms of both sides to solve for the unknown power.
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Frequently asked questions
What is the number 'e'?
The number 'e' is a mathematical constant approximately equal to 2.71828. It is the base of the natural logarithm and arises naturally in many areas of mathematics and science.
How are logarithms used in real life?
Logarithms are used in many real-life applications, such as measuring the intensity of earthquakes (the Richter scale), the acidity of solutions (pH scale), and the loudness of sounds (decibels).