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. Because of the nonlinear scaling of the axes, a function of the form y = axb will appear as a straight line on a log-log graph, in which b will be the slope of the line (gradient) and a will be the y value corresponding to x=1. These graphs are useful when the parameters a and b need to be estimated from numerical data, and can also be used to estimate the fractal dimension of a naturally occurring fractal. These graphs are also extremely useful when data is gathered by varying the control variable along an exponential fashion. In this case, log-log graphing will yield a graph that shows the data points as evenly spaced, despite the compression of points at the low end.
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