The inverse of y = ax is y = log ax.

This means that the graphs of the two functions will be reflections of each other in the line y = x.

e.g. y = 2x and its inverse y = log 2x.


The y-axis is an asymptote for y = log 2 x

Graphs of this type pass through the point (1, 0)

Transformations of the Logarithmic Functions

In a similar manner to other graphs the functions shown above can be transformed.


For y = 3log 2 x the 3 makes the graphsteeper.

For y = log 2x + 2 the graph is moved up by 2 units.

For y = log 2(x + 2) the graph is moved back2 units.

For y = − log 2the graph is reflected in the x-axis.


Two Special Logarithmic Functions

The two logaritmic functions whose values are available from calculators are y = log10 x and y = log e x.

These two functions are the inverses of y = 10x and y = ex respectively.


The equivalent buttons on the Casio fx-82TL calculator are:

Y11_Logarithmic_Functions_05.gif for the function y = log10 x (written as log x and known as common logs)

Y11_Logarithmic_Functions_06.gif for the function y = log e x (written as ln x and known as natural logs)