A Level Maths: Exponentials and Logarithms Topic Summary and Resources
Video Lessons
Watch alongside the worksheet for the full lesson experience, then test your understanding with the lesson questions.
Revision Notes
Handwritten notes summarising the key ideas for each lesson. Ideal for quick review before a test.
Exam Questions
Past-paper-style questions organised by topic, with full mark schemes.
- Laws of Logarithms and Logarithmic Equations (OCR)
- Laws of Logarithms and Logarithmic Equations (Edexcel)
- Solving Exponential Equations (OCR)
- Solving Exponential Equations (Edexcel)
- Exponential and Logarithmic Equations (OCR)
- Exponential Modelling (OCR)
- Exponential Modelling (Edexcel)
- Reduction To Linear Form (OCR)
- Reduction To Linear Form (Edexcel)
Drawn from OCR and Edexcel past papers but designed to be useful for students of all UK exam boards — including AQA and OCR MEI — unless a sheet is explicitly board-specific.
Before You Start This Topic
It will help if you are confident with the following:
- Indices — the index laws underpin the laws of logarithms and exponential algebra
- Quadratic Equations — stealth quadratics often appear in log and exponential equations
- Straight Line Geometry — needed for interpreting logarithmic graphs
A Level Maths exponentials and logarithms is a high-value topic introducing the function $y = a^x$ and its inverse, the logarithm. These tools model an enormous range of real-world situations — population growth, radioactive decay, compound interest, drug concentration — and the algebra of logs lets you solve equations that would otherwise be impossible.
You learn the laws of logarithms: $\log(xy) = \log(x) + \log(y)$, $\log(x/y) = \log(x) – \log(y)$, and $\log(x^k) = k\log(x)$. These let you rearrange and solve equations of the form $a^x = b$ by taking logs of both sides. You meet the special number $e$ and its natural logarithm $\ln(x)$, and learn that the gradient of $e^{kx}$ is $ke^{kx}$ — why the exponential model is so natural for situations where rate of change is proportional to size. You handle modelling problems involving exponential growth and decay, find the constants from given data, and use logarithmic graphs (plotting $\log y$ against $\log x$ or against $x$) to estimate parameters in power and exponential relationships.
Exponentials and logarithms are part of the Pure Maths strand of A Level Maths for AQA, Edexcel, OCR, and OCR MEI students.
Watch out for…
A few things to be careful with: $\log(x + y)$ is NOT $\log(x) + \log(y)$ — the addition law applies to $\log(xy)$, not $\log(x + y)$; the domain of $\log(x)$ is $x > 0$, so check for and discard any solutions that make the argument of a log zero or negative; $\ln(e^x) = x$ and $e^{\ln x} = x$ — these inverse relationships are heavily tested; and when modelling with exponentials, interpret 'initial' as $t = 0$ and check whether your model predicts physically reasonable behaviour as $t$ becomes large.