IBMaths: AA HLDPRevision Notes1. Number & Algebra1.2 Exponentials & Logs1.2.1 Introduction to Logarithms

Introduction to Logarithms (DP IB Maths: AA HL)

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Introduction to Logarithms

What are logarithms?

  • A logarithm is the inverse of an exponent
    • If a to the power of x equals b then log subscript a open parentheses b close parentheses equals x where a > 0, b > 0, a ≠ 1
      • This is in the formula booklet
      • The number a is called the base of the logarithm
      • Your GDC will be able to use this function to solve equations involving exponents
  • Try to get used to ‘reading’ logarithm statements to yourself
    • log subscript a left parenthesis b right parenthesis space equals space x would be read as “the power that you raise a to, to get b, is x”
    • So log subscript 5 125 space equals space 3 would be read as “the power that you raise 5 to, to get 125, is 3”
  • Two important cases are:
    • ln space x equals log subscript straight e open parentheses x close parentheses
      • Where e is the mathematical constant 2.718…
      • This is called the natural logarithm and will have its own button on your GDC
    • log space x equals log subscript 10 open parentheses x close parentheses
      • Logarithms of base 10 are used often and so abbreviated to log x

Why use logarithms?

  • Logarithms allow us to solve equations where the exponent is the unknown value
    • We can solve some of these by inspection
      • For example, for the equation 2x = 8 we know that x must be 3
    • Logarithms allow use to solve more complicated problems
      • For example, the equation 2x = 10 does not have a clear answer
      • Instead, we can use our GDCs to find the value of log subscript 2 10

Examiner Tip

  • Before going into the exam, make sure you are completely familiar with your GDC and know how to use its logarithm functions

Worked example

Solve the following equations:

i)
x equals log subscript 3 27,
 

ai-sl-1-1-2intro-to-logs-we-i

ii)
2 to the power of x equals 21.4, giving your answer to 3 s.f.
 
ai-sl-1-1-2intro-to-logs-we-ii

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    Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.