ASMaths: PureEdexcelRevision Notes6. Exponentials & Logarithms6.2 Laws of Logarithms6.2.2 Exponential Equations

Exponential Equations (Edexcel AS Maths: Pure)

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Paul

Last updated

23 April 2023

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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”

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 (log_e) 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
- 4^x = (2²)^x = 2^2x = (2^x)²
- e^2x = (e²)^x = (e^x)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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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.