Exponentials & Logarithms — A-Level Mathematics Revision
Revise Exponentials & Logarithms for A-Level Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.
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Go to DifferentiationWhat 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 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.
Exponentials & Logarithms exam questions
Exam-style questions for Exponentials & Logarithms with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel and OCR specifications.
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Exponentials & Logarithms
Core concept
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 involvi…
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).