Introduction to Logarithms (DP IB Maths: AA HL)

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