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 y = a x k {displaystyle y=ax^{k}} – appear as straight lines in a log–log graph, with the power term corresponding to the slope, and the constant term corresponding to the intercept of the line. 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. 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 y = a x k {displaystyle y=ax^{k}} – appear as straight lines in a log–log graph, with the power term corresponding to the slope, and the constant term corresponding to the intercept of the line. 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 y = a x k , {displaystyle y=ax^{k},} taking the logarithm of the equation (with any base) yields: Setting X = log ⁡ x {displaystyle X=log x} and Y = log ⁡ y , {displaystyle Y=log y,} which corresponds to using a log–log graph, yields the equation: where m = k is the slope of the line (gradient) and b = log a is the intercept on the (log y)-axis, meaning where log x = 0, so, reversing the logs, a is the y value corresponding to x = 1.