SEMI-LOG AND LOG-LOG
Let’s take a closer look at the differences between semi-log and log-log graphs.
PLOTTING ON LOGARITHMIC PAPER
Logs are helpful when plotting certain types of data. There are two types of log graphs that can
be used when plotting data.
Semi-log Graph
The first is called a semi-log graph. In a semi-log graph the y-axis is logarithmic, which means
the separation between the ticks on the graph is proportional to the logarithm of numbers. The xaxis has a linear scale, which means the ticks are evenly spaced.
A semi-log graph is useful when graphing exponential functions. Consider a function of the
form y  ba . When graphed on semi-log paper, this function will produce a straight line with
x
slope log(a) and y-intercept log(b).
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Example: Plot the function
y  5x on an ordinary axis (x- and y- linear scales) as well as on a
semi-log axis.
Solution:
Both functions below:
(Ordinary axis)
(semi-log axis)
_______________________________________________________________________ Log-log Graph
The second type is called a log-log graph. In a log-log graph, both the x-axis and the y-axis are
logarithmic.
This is useful for determining power relationships. If a function of the form y  ax is graphed
n
on log-log paper, a straight line will be produced, with slope n and y-intercept log(a).