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 2x the 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:
for the function y = log10 x (written as log x and known as common logs)
for the function y = log e x (written as ln x and known as natural logs)