Logarithmic scale

A scale on which equal distances represent equal ratios rather than equal differences. It compresses wide ranges of values and makes multiplicative change appear as additive distance.

Logarithm: The inverse operation of exponentiation, mapping a number to the exponent required to produce it from a chosen base. Its values determine the positions assigned to numbers on a logarithmic scale.
Decibel: A logarithmic unit expressing a ratio of power or, with a specified convention, related quantities such as sound pressure. Sound levels use logarithms to represent vast intensity ratios compactly.
Linear scale: A scale on which equal distances represent equal differences in the values shown. It allocates equal space to equal increments, unlike this scale’s equal-ratio spacing.
Ratio: A comparison of two quantities by division. The scale’s equal steps encode equal ratios between successive values.
Geometric progression: A sequence in which each term after the first is obtained by multiplying the previous term by a fixed nonzero ratio. Equal steps on the scale correspond to successive terms with a constant ratio.
Richter magnitude scale: A historical logarithmic scale for earthquake magnitude based on seismic-wave amplitudes. Each whole-number increase represents a tenfold increase in recorded wave amplitude.
Semilogarithmic plot: A graph with one logarithmic axis and one linear axis. It combines logarithmic compression in one variable with ordinary spacing in another.
Order of magnitude: A rough measure of size expressed as a power of ten. Decade markings group values by their logarithmic distance from one another.
Logarithmic spiral: A spiral whose distance from its center grows exponentially with its angle. Its geometry turns equal angular changes into equal multiplicative changes in radius.
pH: A measure of acidity defined as the negative base-ten logarithm of hydrogen-ion activity. Its values compress hydrogen-ion activities spanning many orders of magnitude.

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