Log-log graph
Encyclopedia
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. Because of the nonlinear scaling of the axes, a function of the form
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.
of a naturally occurring fractal
. Notably, when a probability distribution
follows a power law
, it will appear as a line on a log-log scale. These graphs are also extremely useful when data are 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.
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...
and engineering
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...
, a log-log graph or log-log plot is a two-dimensional graph of numerical data that uses logarithmic scale
Logarithmic scale
A logarithmic scale is a scale of measurement using the logarithm of a physical quantity instead of the quantity itself.A simple example is a chart whose vertical axis increments are labeled 1, 10, 100, 1000, instead of 1, 2, 3, 4...
s on both the horizontal and vertical axes. Because of the nonlinear scaling of the axes, a function of the form
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.Applications
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 dimensionFractal dimension
In fractal geometry, the fractal dimension, D, is a statistical quantity that gives an indication of how completely a fractal appears to fill space, as one zooms down to finer and finer scales. There are many specific definitions of fractal dimension. The most important theoretical fractal...
of a naturally occurring fractal
Fractal
A fractal has been defined as "a rough or fragmented geometric shape that can be split into parts, each of which is a reduced-size copy of the whole," a property called self-similarity...
. Notably, when a probability distribution
Probability distribution
In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....
follows a power law
Power law
A power law is a special kind of mathematical relationship between two quantities. When the frequency of an event varies as a power of some attribute of that event , the frequency is said to follow a power law. For instance, the number of cities having a certain population size is found to vary...
, it will appear as a line on a log-log scale. These graphs are also extremely useful when data are 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.