Log–log plot: Difference between revisions

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{{Short description|2D graphic with logarithmic scales on both axes}}

{{More citations needed|log graph papers and their use|find=https://www.mathnstuff.com/math/spoken/here/2class/340/loggraf.htm|date=August 2025|name=Agnes (A²) Azzolino}}

{{More citations needed|date=December 2009}}

[[Image:LogLog exponentials.svg|class=skin-invert-image|thumb|A log–log plot of ''y''&nbsp;=&nbsp;''x''&nbsp;(blue), ''y''&nbsp;=&nbsp;''x''²&nbsp;(green), and ''y''&nbsp;=&nbsp;''x''³&nbsp;(red).<br>Note the logarithmic scale markings on each of the axes, and that the log&nbsp;''x'' and log&nbsp;''y'' axes (where the logarithms are 0) are where ''x'' and ''y'' themselves are 1.]]

[[File:Comparison of simple power law curves in original and log-log scale.png|class=skin-invert-image|thumb|Comparison of linear, concave, and convex functions when plotted using a linear scale (left) or a log scale (right).]]

[[File:Loglog graph paper.gif|thumb|blank log-log graph paper]]

In [[science]] and [[engineering]], a '''log–log graph''' or '''log–log plot''' is a two-dimensional graph of numerical data that uses [[logarithmic scale]]s on both the horizontal and vertical axes. [[Exponentiation#Power_functions|Power functions]] – relationships of the form <math>y=ax^k</math> – appear as straight lines in a log–log graph, with the exponent corresponding to the slope, and the coefficient corresponding to the intercept. Thus these graphs are very useful for recognizing these relationships and [[estimating parameters]]. Any base can be used for the logarithm, though most commonly base 10 (common logs) are used.