Log–log plot

In science and engineering, a log–log graph or log–log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes. Monomials – relationships of the form ${\displaystyle y=ax^{k}}$ – appear as straight lines in a log–log graph, with the power and constant term corresponding to slope and intercept of the line, and thus these graphs are very useful for recognizing these relationships and estimating parameters. Any base can be used for the logarithm, though most common are 10, e, and 2.

Given a monomial equation ${\displaystyle y=ax^{k},}$ taking the logarithm of the equation (with any base) yields:

Setting ${\displaystyle X=\log x}$ and ${\displaystyle Y=\log y,}$ which corresponds to using a log–log graph, yields the equation:

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