## Graph of a Log Function

This interactive GeoGebra worksheet allows you to see what the graph of y=log_{a}(x) looks like for values of a from 0.1 to 10 by moving the slider. Have a go and see what happens!

You should note the following.

If a>1, then:

- As x increases so does y.
- y is only defined for positive values of x.
- As x gets close to zero, y gets very large and negative.
- log
_{a}(x) is negative if x is less than one and positive if x is greater than one. - log
_{a}(1)=0. - As a decreases, the graph gets steeper.

If 0<a<1, then:

- As x increases y decreases.
- y is only defined for positive values of x.
- As x gets close to zero, y gets very large and positive.
- log
_{a}(x) is positive if x is less than one and negative if x is greater than one. - log
_{a}(1)=0. - As a increases, the graph gets steeper.

If a=1 then the graph does not exist.

If you want to see approximately what the graph of the natural logarithm looks like then let a=2.7 (remember that e=2.718...).

If you want to return the slider to its original position, then simply click on the icon in the top right hand corner of the worksheet.

## Contact the Maths Support Centre

James Joyce Library, University College Dublin, Belfield, Dublin 4, Ireland. T: +353 1 716 7536 | E: msc@ucd.ieIf you enter the library the MSC is the glass room with the orange and green circles just to the left opposite the entrance. You will need your valid student card to gain access to the James Joyce Library.