A-Level Maths: Exponentials & Logarithms Revision

Exponentials & Logarithms is a core part of A-Level Maths. Revise the key concepts and common mistakes below, then lock them in with the free games.

Key concepts

Exponential functiony = aˣ with a > 0, a ≠ 1. Grows rapidly if a > 1; decays if 0 < a < 1. Always passes through (0, 1).

Natural exponentialy = eˣ where e ≈ 2.71828. Unique property: d/dx(eˣ) = eˣ. Used for continuous growth/decay.

Logarithmlogₐ x is the inverse of aˣ: logₐ x = y ⟺ aʸ = x. Natural log: ln x = logₑ x.

Log lawslog(xy) = log x + log y; log(x/y) = log x − log y; log(xⁿ) = n log x. Same base throughout.

Change of baselogₐ x = logᵦ x / logᵦ a. Useful when calculator only has log₁₀ or ln.

Modelling exp/logPopulation growth, radioactive decay, Newton's law of cooling: all use y = Aeᵏᵗ. Log transforms linearise data.

Test yourself with these quick revision games for this topic: