A LevelMaths: Pure 3CIERevision Notes2. Logs & Exponentials2.2 Laws of Logarithms2.2.2 Exponential Equations

Exponential Equations (CIE A Level Maths: Pure 3)

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Exponential Equations

What are exponential equations?

Exponential Equations Notes fig1, A Level & AS Maths: Pure revision notes

  • An equation where the unknown is a power
  • In simple cases the solutions can be “spotted” Exponential Equations Notes fig2, A Level & AS Maths: Pure revision notes

How do I solve exponential equations?

  • Laws of Indices are often needed to rewrite equations
  • Laws of Logarithms are used to solve exponential equations
  • ln (loge) is often used
  • Answers are often written in terms of ln

Exponential Equations Notes fig4, A Level & AS Maths: Pure revision notes

Exponential Equations Notes fig5, A Level & AS Maths: Pure revision notes

Exponential Equations Notes fig3, A Level & AS Level Pure Maths Revision Notes

What about hidden quadratics?

  •  Look out for “hidden” squared terms, these are hidden quadratics which will need to be solved
    • 4x = (22)x = 22x = (2x)2
    • e2x = (e2)x = (ex)2

Exponential Equations Notes fig6, A Level & AS Maths: Pure revision notes

Worked example

Exponential Equations Example fig1, A Level & AS Maths: Pure revision notes

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    Paul

    Author: Paul

    Expertise: Maths

    Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team.