On Logarithmic Scales

During the semester, I expect that we will be using logarithmic scales. For those of view that are interested in a quick review of what logarithmic scales are, you may find a couple of nice explanations at the Math Forum here: http://mathforum.org/library/drmath/view/55520.html

I highlight the following:
First, let's look at a semi-log graph. Here, the horizontal axis represents x as usual, but the vertical position is not y units from the axis but log(y), which I'll call Y to make notation easier. (You can use any base you want for the log, but I'll assume base ten.) If you draw a straight line on this graph, then it has an equation of the form

    Y = ax + b
which means
log(y) = ax + b
Now, if you raise 10 to the power on each side of this equation, you get
y = 10^(ax + b)
  = 10^(ax) * 10^b
  = k 10^(ax)

where k = 10^b. So if you expect two variables to have an exponential relationship, you
just have to plot them on semi-log paper, find the best-fit line, and use its slope and
intercept to find the parameters for the equation.

Often, percent change is what is important.
On standard axes, an equal QUANTITY of change is an equal amount of  space. On log
axes, an equal PERCENT change is an equal amount of space. You can thus use your
eyes to quickly compare percent growth or percent change, instead of having to correct
for the magnitude of the data. That is, 10 and 12 will be equally far apart as 50 and 60
on log axes, because each is a 20% increase.

Source: Math Forum: http://mathforum.org/library/drmath/view/55520.html