Graphing logarithmic functions
Example:
Graph the logarithmic function y= log2x
Solution:
We can give different values for x and find out the values of y as shown in the following table.
| x | y |
| 0.25 | -2 |
| 0.5 | -1 |
| 1 | 0 |
| 2 | 1 |
| 4 | 2 |
| 8 | 3 |
The graph is shown below:
As we can see from the above graph, x is increased exponentially as y is increased. This is
because the function is exponential. We can also write it in the form x = 2y
Example:
How does the function y= log2(x-3) look in the domain of [3 8]?
Solution:
Again we can give different values of x and find the values of y as shown in
the this table.
| x | y |
| 3 | -infinity |
| 4 | 0 |
| 5 | 1 |
| 6 | 1.585 |
| 7 | 2 |
| 8 | 2.32 |
The graph can be shown as following:
When x is four, the value of y is zero and from there onwards, the graph increases exponentially. This is because the function is exponential and can also be written:
x = 2y + 3