This applet displays Exponential and Logarithmic Function Graphs (study between 0 and 1). These functions are inverses, i.e., the coordinate (x, y) of one is the coordinate of (y, x) with the other. The bases examined in this demo are some of the more common integer values with the exception of the natural number, ℯ. These bases are {1,2,ℯ,3,4,5,6,7,8,9,10,11,12}.
One part of the purpose of this applet is to illustrate the GeoGebra command set for these functions.

1) Students need to create a table with the following columns for each function:
Base x-value y-value function equation
2) Compare the values recorded in the exponential columns to the logarithmic columns. State the differences and similarities you notice between the different functions.
3) Click on the y = x check box to draw the Identity Function on the screen. Can you determine any relationship to this line and the points A and B after cycling through the different bases.
4) Click the Segment AB check box to draw segment AB between points A and B. Examine the textbox which comes up when cycling through the different bases.
This applet can be used by teachers in a demonstration mode in the classroom or teachers can have students load it on their own computers as a worksheet to be completed for a grade.