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LearnAQA7357First teaching 2017Paper 1 · PureExponentials and logarithms
Paper 1 · Module

Exponentials and logarithms

5 subtopics≈ 200 min in total
Start the module: Laws of logarithmsOpen graphing calculator

  1. Laws of logarithms

    What a logarithm is (the power you need), the three laws that come straight from the index laws, and how to combine and simplify logarithms, including ln⁡\ln and lg⁡\lg.

    ≈ 40 min

  2. The functions eˣ and ln x

    Meet e≈2.718e\approx2.718, the most natural base for growth, and its inverse ln⁡x\ln x: their graphs, asymptotes and intercepts, transformations, inverses and exact answers.

    ≈ 40 min

  3. Exponential equations and inequalities

    Bringing an unknown power down with logarithms: solving ax=ba^x=b, equations with xx in two powers, disguised quadratics, and inequalities like "the smallest nn such that 0.8n<0.10.8^n<0.1".

    ≈ 40 min

  4. Logarithmic equations

    Solving equations with the unknown inside a logarithm: combine with the log laws, remove the logs by raising to a power, and always check that the answers are in the domain.

    ≈ 35 min

  5. Exponential models and linear forms

    Using logarithms in the real world: modelling growth and decay with AektAe^{kt}, and turning curves like y=kxny=kx^n and y=kaxy=ka^x into straight lines so their constants can be read from a graph.

    ≈ 45 min
AQA 7357 Exponentials and logarithms — A Level Mathematics · Salam Academy