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Cambridge AS & A Level Mathematics

2.2, 3.2Logarithmic and exponential functions

Logarithmic and exponential functions in Cambridge AS & A Level Mathematics: what the syllabus expects you to know, the learning objectives and how to practise.
Topic54 practice questions3 lessons

Learning objectives

What the syllabus expects you to be able to do.

  1. 3.2.1Papers 2 and 3: relate logarithms to indices and use the laws of logarithms (excluding change of base).
  2. 3.2.2Papers 2 and 3: understand the definition, properties and graphs of eˣ and ln x as inverse functions.
  3. 3.2.3Papers 2 and 3: use logarithms to solve equations and inequalities in which the unknown appears in an index.
  4. 3.2.4Papers 2 and 3: transform a relationship to linear form with logarithms and find unknown constants from the gradient or intercept.

Lessons

  • Exponential and logarithmic functions: e^x and ln x

    40 min

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  • Laws of logarithms and equations with unknown indices

    40 min

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  • Reducing relationships to linear form

    40 min

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Sample question

A sample question on this topic. Answer it, check it, then read the worked answer.

Logarithmic and exponential functions: sample question

1 mark

Solve ex=15\mathrm{e}^{x} = 15, giving your answer to 3 significant figures.

Complete: x = …

Only if the answer has a unit, e.g. cm or km/h.

Turn Logarithmic and exponential functions into a strength.

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