LogLogSkala

LogLogSkala is a plotting scale in which both axes are presented on logarithmic scales. It is commonly used to visualize relationships that span multiple orders of magnitude and to identify power-law behavior, which may be difficult to discern on linear scales.

In a LogLogSkala, a relationship of the form y = a x^b is transformed into a straight line in the log-log coordinate system. The slope of this line equals the exponent b, while the intercept relates to the coefficient a. The choice of logarithm base (for example base 10 or natural logarithm) does not change the qualitative interpretation, though it affects the numerical values of the coordinates.

Practically, data with zero or negative values cannot be plotted directly on a log-log scale, since the logarithm is undefined for zero and negative numbers. Analysts often exclude such points or apply data transformation or shifting. The log-log transformation can also alter error distributions and sensitivity to measurement noise, so interpretation should consider potential biases and data quality. Curvature on a log-log plot typically indicates deviations from a pure power-law relationship.

Common applications include detecting power-law distributions and scaling relationships in physics, biology, economics, and network science. For example, straight-line behavior on a log-log plot can indicate Zipf or Pareto-type distributions or allometric scaling in biology.

See also: logarithmic scale, semi-log plot, power law, allometry.