For reference, here is a table of values for `y=5^x`:

 x −1 0 1 2 3 4 y 0.2 1 5 25 125 625

Here is the graph on linear x-y axes:

Open image in a new page

Graph of `y=5^x` on linear-linear axes.

Our plot shows reasonable detail for values of `x` greater than `1` only.

Here's the same data plotted on semi-logarithmic (log-lin) axes.

Open image in a new page

Graph of `y=5^x` on semilogarithmic (log-lin) axes.

You can see a lot more detail for smaller values of `x` and `y`.

Notice that the graph of an exponential function on a semi-log graph is a straight line.

Notice also that the numbers along the x axis are evenly spaced, while along the y-axis, we have powers of 10 evenly spaced.

Finally, here's the graph of `y=5^x` on lin-log (linear vertical axis, logarithmic horizontal axis).

Open image in a new page

Points along the curve `y=5^x` using lin-log axes.

In this example, there is not a lot of advantage in using this last semilogarithmic graph type, as we don't see much detail for values less than `1`.