Logarithmic Functions (Edexcel International AS Maths): Revision Note

Dan Finlay

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Logarithmic Functions

Logarithmic functions

Logarithmic Functions Notes fig1, A Level & AS Maths: Pure revision notes
  • a = bx and log b a = x are equivalent statements

  • a > 0

  • b is called the base

  • Every time you write a logarithm statement say to yourself what it means

    • log3 81 = 4

      “the power you raise 3 to, to get 81, is 4”

    • logp q = r

      “the power you raise p to, to get q, is r

 

Logarithm rules

  • As a logarithm is the inverse of raising to a power

    Logarithmic Functions Notes fig2, A Level & AS Maths: Pure revision notes

How do I use logarithms?

Logarithmic Functions Notes fig3, A Level & AS Level Pure Maths Revision Notes
  • Recognising the rules of logarithms allows expressions to be simplified

Logarithmic Functions Notes fig4, A Level & AS Maths: Pure revision notes
  • Recognition of common powers helps in simple cases

    • Powers of 2: 20 = 1, 21 = 2, 22 = 4, 23 = 8, 24 =16, …

    • Powers of 3: 30 = 1, 31 = 3, 32 = 9, 33 = 27, 34 = 81, …

    • The first few powers of 4, 5 and 10 should also be familiar

  • For more awkward cases a calculator is needed

Logarithmic Functions Notes fig5, A Level & AS Level Pure Maths Revision Notes
  • Calculators can have, possibly,  different logarithm buttons

Logarithmic Functions Notes fig6, A Level & AS Maths: Pure revision notes
  • This button allows you to type in any number for the base

Logarithmic Functions Notes fig8, A Level & AS Maths: Pure revision notes
  • Shortcut for base 10 although SHIFT button needed 

  • Before calculators, logarithmic values had to be looked up in printed tables

Notation 

  • 10 is a common base

    • log10 x is abbreviated to log x or lg x

  • (log x)2 ≠ log x2

Worked Example

Logarithmic Functions Example fig1, A Level & AS Maths: Pure revision notes
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Dan Finlay

Author: Dan Finlay

Expertise: Maths Subject Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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