#
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

http://www.nd.edu/~mjm/

It is copyrighted to the extent allowed by which ever laws pertain to the World Wide Web and the Internet.

I would hope that as a professional courtesy, this notice remain visible to other users.

There is no charge for copying and dissemination.

Version: 6/19/00

More recent versions of this notebook may be available at:

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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 + b2

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.

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Linear plots

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Linear plots are not appropriate

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Logarithmic relations

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Semilog Plots

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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