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Power Law


A power law is a functional relationship of the form

 y=Cx^a,

where C and a are constants. scaling the argument by a positive factor lambda scales the value by lambda^a, since y(lambdax)=lambda^ay(x). Taking logarithms gives

 lny=lnC+alnx,

so a power law appears as a line of slope a on a log-log plot.


See also

Least Squares Fitting--Power Law, Log-Log Plot, Scaling

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References

Schroeder, M. Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise. New York: W. H. Freeman, 1991.

Cite this as:

Weisstein, Eric W. "Power Law." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PowerLaw.html

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