Google Classroom
GeoGebraGeoGebra Classroom

2A-2. Logarithmic Functions

Instructions:

  • Use the input boxes and slider tools for and to set the parameters for the logarithmic function .
  • Use the input box for to adjust the location of the point on the graph. Use the slider tool for to adjust the location of the point .

Logarithmic Functions

Logarithmic functions are inverses of exponential functions.
  • Algebraically, this means that they "undo" the operation of an exponential function. This allows us to "cancel" and solve equations.
  • Graphically, this means that the graph of a logarithm function is a reflection about the line y = x of the corresponding exponential function (because inverse functions swap inputs x and outputs y).
We will primarily work with the natural logarithm, , which is the inverse of the natural exponential function, . Notice the relationship between the behaviors of these two functions.