Primer on Log-Log and Log-Linear (semi-log) Plots

This notebook has been written in  Mathematica by

Mark J. McCready
Professor and Chair of Chemical Engineering
University of Notre Dame
Notre Dame, IN 46556
USA


[Graphics:Images/log_log_gr_1.gif]
http://www.nd.edu/~mjm/


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Version: 6/19/00
More recent versions of this notebook may be available at:
[Graphics:Images/log_log_gr_2.gif]

Motivation

Once you have done dimensional analysis and produced 2-3 dimensionless groups or if you are just using someone else's correlation, you may find that you need to use or produce a graphical representation of the model.  

If the model is such that there are two parameters and they are linearly related, then you will be happy to plot the model on a regular (linear) axis plot and you the result.  Even if you cook up some kind of polynomial fit, a linear plot is appropriate.

If y = m x + b  or

y = b0 + b1 [Graphics:Images/log_log_gr_3.gif] + b2 [Graphics:Images/log_log_gr_4.gif]

However, if the dimensionless groups related by a power law or exponential function, it is convenient to use log-log or semilog plots to show the results.

This notebook gives examples of how to do this and shows why it is useful.

Linear plots
Linear plots are not appropriate
Logarithmic relations
Semilog Plots

Conclusions

We have seen that power law relations are best plotted on Log-Log plots which are recognizable because of the graduations of the axes.  

Further, if there is an exponential or log relation between the variables, a semilog plot, where one of the axes is log and the other is linear is appropriate.  


Converted by Mathematica      June 19, 2000