Logarithmic functions > Logarithmic functions
12345Logarithmic functions

Theory

Take a look at the applet: Logarithmic function

A function of the form f ( x ) = g log ( x ) is called a logarithmic function. In this function, g > 0 and g 1 is a fixed given base.

The graphs of the functions y = g x en y = g log ( x ) are mirror images of each other with respect to the line y = x . They are inverse functions of each other.

You can therefore derive the characteristics of y = g log ( x ) from those of y = g x :

  • the domain is 0, ;

  • the range is ;

  • the graph is increasing while g > 1 , and decreasing while 0 < g < 1 ;

  • the y -axis is the vertical asymptote of the graph.

All functions that can be derived from transformations of y = g log ( x ) are called logarithmic functions.

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