9: Summary

If your data differs by a couple orders of magnitude or more, then an ordinary graph will make your data look “squashed”, and you might want to think about a log-transformation. There are two ways you can do this.

  1. Take the log of each number, and then make a normal graph.
  2. Make a graph, and let the paper “take the log” of the number.

In either case your graph will have the same shape.

As an added bonus, IF your data represents an exponential growth or decay process, THEN log-transforming it will turn the graph into a straight line. (The slope of the line will even give you a hint as to the rate of the exponential growth or decay, although we didn’t get into this.)

Semi-log paper is tricky to use at first. It is divided into “cycles,” which are themselves divided into 10 pieces. The lines get closer together at the top of the cycle, because the numbers are arranged on a log scale. Each cycle starts at a multiple of ten, and it’s NOT possible to get to zero.

Learning outcomes

Now that you have done this module you should be able to:

  • Explain how log-transformation turns graphs of exponential growth into straight lines.
  • Explain log-transformation of data into graphs by two methods:
    • Log then graph: take the log of the data and then graph the transformed data in normal graph paper or,
    • Graph then log: graph the untransformed data on semi-log paper and let the paper “take the log” of the data.

If you want a printer-friendly version of this module, you can find it here in a PDF document. This printer-friendly version should be used only to review, as it does not contain any of the interactive material, and only a skeletal version of problems solved in the module.