The inverse of y = a^{x} is y = log _{a}x.

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

e.g. y = 2^{x} and its inverse y = log _{2}x.

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 steeper.For up by 2 units. |
For back2 units.For reflected in the x-axis. |

### Two Special Logarithmic Functions

The two logaritmic functions whose values are available from calculators are y = log_{10} x and y = log_{ e} x.

These two functions are the inverses of y = 10^{x} and y = e^{x} respectively.

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

for the function y = log

_{10}x (written as log x and known ascommonlogs)for the function y = log

_{ e}x (written as ln x and known asnaturallogs)