logscales

Log scales, or logarithmic scales, are axis scales in which equal distances on the axis correspond to multiplying by the same factor. The scale is based on a logarithm with a chosen base, most commonly base 10, base e, or base 2.

On a base-10 log scale, tick marks and labels follow powers of ten (1, 10, 100, 1000). Differences on the axis represent orders of magnitude rather than additive increments. This makes multiplicative relationships easier to see and allows data spanning several orders of magnitude to be visualized in a compact form.

Variants include semi-log plots, where only one axis is logarithmic, useful for displaying exponential growth; and log-log plots, where both axes are logarithmic, which linearize power-law relationships of the form y = k x^n. In both cases, a straight line indicates a simple mathematical relationship, with slope corresponding to the logarithmic rate of change.

Applications and advantages: log scales are widely used in science, engineering, economics, and data visualization when the data cover wide ranges, when multiplicative processes are more natural, or when relative changes matter. They also help stabilize variance and reveal proportional growth patterns.

Limitations and considerations: log scales cannot display zero or negative values directly; base choice affects tick labeling and slope interpretation; care is needed when converting back to linear values; not all datasets benefit from log scaling.