A-Level Exponentials & Logarithms Revision
Exponentials and logarithms revision for A-Level and International A-Level Maths
Logarithms are the topic students most often describe as clicking suddenly. Before it clicks, every question looks like a different trick; afterwards, almost all of them are the same idea — a logarithm is the power you raise the base to, and the laws simply let you rearrange until the unknown is on its own. This free revision engine covers the exponentials and logarithms content of Edexcel A-Level Maths and the International A-Level Pure 2 and Pure 3 papers, and gives you enough varied practice for that click to happen.
What the exponentials and logarithms revision engine covers
Exponential functions and graphs — the shape of y = aˣ, its asymptote, and transformations Introducing logarithms — converting between exponential and logarithmic form The laws of logarithms — adding, subtracting and bringing down a power Solving equations using logarithms — taking logs of both sides, and hidden quadratics Changing the base — the change of base formula and equations mixing two bases Natural logarithms and e — ln and eˣ as inverse functions Exponential growth and decay — modelling with N = Ae^(kt), and finding a rate or a half-life Logarithmic graphs and linear form — reducing y = axⁿ or y = abˣ to a
Logarithm laws and results you need to know
The definition. If aˣ = b then log to base a of b equals x. A logarithm is a power. The addition law. Adding two logs of the same base multiplies their arguments. The subtraction law. Subtracting two logs of the same base divides their arguments. The power law. A coefficient in front of a log becomes a power inside it, and vice versa. Two results worth memorising. log to base a of a is 1, and log of 1 is 0 in any base. Change of base. A log in one base can be rewritten as a quotient of logs in any other base. Natural logs. ln x means log to base e, and ln and eˣ undo each other exactly. ln e = 1 and ln 1 = 0. Growth and decay. In N = Ae^(kt), A is the value at t = 0. A positive k grows, a negative k decays, and a half-life is found by setting N to half of A. Linear form. For y = axⁿ, plotting log y against log x gives a straight line with gradient n. For y = abˣ, plot log y against x instead, and the gradient is log b.
How to use it
Pick a topic or an exam module. Answers are marked mathematically, so an exact answer such as ln 8 and its decimal equivalent both count as correct where the question allows either. Two hints per question steer you towards the right law without solving it for you.
More A-Level Maths revision
Logarithms reappear throughout the course — in differentiating and integrating ln x, and in solving the equations that come out of growth and decay models. See every topic and your progress on the revision hub. All engines are free to use.