MathBench > Visualization

Log Transformations

Logs of graphs and Graphs of logs

In this module we're going to discuss ways of combining logs and graphics. You remember logs, right? Just in case you don't, here are 2 pictures of logs again:

A size 5 log

Log(100,000) = 5

A size 9 log

Log(1,000,000, 000) = 9

log(100,000) = 5 log(1,000,000,000) = 9


Remember that the log of the measurement basically tells you how much space that number takes up.

If the measurement is bigger than one, it "takes up space" in front of the decimal and the log is positive. A 6-digit number has a log of 5-point-something. A 10-digit number has a log of 9-point-something.

If the measurement is smaller than one, it only "takes up space" AFTER the decimal point, and the log is negative.

A measurement of zero doesn't take up any space before OR after the decimal point, and it has no log. Neither does a negative measurement. That's okay, because usually we're using logs to measure things size, weight, height, or the number of organisms in a population. These measurements can't be negative in any case.

It's all very well to take logs of individual numbers, but what we really want is to be able to visualize these numbers in relation to other numbers. Therefore we need to make graphs. 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.

You guessed it, we're going to look at each of these options below.