Introduction to Logarithms (DP IB Analysis & Approaches (AA)) : Revision Note

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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 Tips and Tricks

  • 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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