A-level maths / Pure 1 / Exponentials and logarithms
Exponentials and logarithms
Understand repeated multiplication, undo an exponential and find a useful model.
Choose a skill below. Move the graphs at your pace, keep the algebra in view and check your answers against worked solutions.
- Exponential graphs and eSketch exponential graphs, identify asymptotes and transformations, differentiate e to a linear power, and solve coefficient and tangent problems.
- Exponential growth and decayUse exponential models, interpret rates and initial values, calculate doubling times and half-lives, solve thresholds and distinguish continuous rates from percentage changes.
- Logarithms and log lawsUnderstand what a logarithm means, calculate exact values, prove and use the product, quotient and power laws, change base and avoid domain errors.
- Natural logarithms (ln)Understand ln as logarithm to base e, use inverse identities, sketch natural logarithm transformations and solve simple equations exactly.
- Exponential and logarithmic equationsSolve exponential and log equations with common bases, logarithms, quadratic substitutions and domain checks. Includes natural logs, reciprocal exponentials and mixed bases.
- Logarithmic graphs for modellingLinearise power and exponential relationships using logarithms. Read transformed axes, recover constants, fit original data and interpret reversed axes and modelling limits.
Useful foundations
Review index laws, graph transformations or quadratic equations when those steps need a refresher.