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

Introduction to Logarithms

What are logarithms?

• A logarithm is the inverse of an exponent

  • If then  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

  • would be read as “the power that you raise to, to get , is ”

  • So  would be read as “the power that you raise 5 to, to get 125, is 3”

• Two important cases are:

  • 

    • Where e is the mathematical constant 2.718…

    • This is called the natural logarithm and will have its own button on your GDC

  • 

    • 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 2^x = 8 we know that x must be 3

  • Logarithms allow use to solve more complicated problems

    • For example, the equation 2^x = 10 does not have a clear answer

    • Instead, we can use our GDCs to find the value of