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Log-Log Plot


A log-log plot displays positive coordinates (x,y) using logarithmic scales on both axes. Any fixed logarithm base may be used without changing whether the plotted points are collinear or changing the fitted power-law exponent. Base 10 is traditional and common for labeled axes, while natural logarithms are often convenient in formulas. A power law y=Cx^a appears as the line

 lny=lnC+alnx,

whose slope is a. Straightness on a log-log plot is therefore useful for diagnosing power-law behavior, although it does not by itself establish a power-law model.

LogLogPlot

The power-law data y=3x^(3/2) form a straight line on the log-log plot above.

The Wolfram Language functions LogLogPlot[f, {x, xmin, xmax}] and ListLogLogPlot[data] produce log-log plots of functions and data, respectively.


See also

Least Squares Fitting--Power Law, Logarithm, Power Law, Semilog Plot

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References

Cleveland, W. S. The Elements of Graphing Data. Summit, NJ: Hobart Press, 1994.

Cite this as:

Weisstein, Eric W. "Log-Log Plot." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Log-LogPlot.html

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