 right|thumb|400px|a log scale makes it easy to compare values which cover a large range, such as in this map. a logarithmic scale is a nonlinear scale used when there is a large range of quantities. common uses include the earthquake strength, sound loudness, light intensity, and ph of solutions. it is based on orders of magnitude, rather than a standard linear scale, so each mark on the scale is the previous mark multiplied by a value. ==common usages== the following are examples of commonly used logarithmic scales, where a larger quantity results in a higher value: * richter magnitude scale and moment magnitude scale (mms) for strength of earthquakes and movement in the earth. * shannon, nat, ban and deciban, for information or weight of evidence; * bel and decibel and neper for acoustic power (loudness) and electric power; * cent, minor second, major second, and octave for the relative pitch of notes in music; * logit for odds in statistics; * palermo technical impact hazard scale; * logarithmic timeline; * counting f-stops for ratios of photographic exposure; * rating low probabilities by the number of 'nines' in the decimal expansion of the probability of their not happening: for example, a system which will fail with a probability of 10â5 is 99.999% reliable: "five nines". * entropy in thermodynamics. * information in information theory. * particle size distribution curves of soil the following are examples of commonly used logarithmic scales, where a larger quantity results in a lower (or negative) value: * ph for acidity and alkalinity; * stellar magnitude scale for brightness of stars; * krumbein scale for particle size in geology. * absorbance of light by transparent samples. some of our senses operate in a logarithmic fashion (weberâfechner law), which makes logarithmic scales for these input quantities especially appropriate. in particular our sense of hearing perceives equal ratios of frequencies as equal differences in pitch. in addition, studies of young children in an isolated tribe have shown logarithmic scales to be the most natural display of numbers by humans. ==graphic representation== [[file:logarithmic scales.svg|thumb|400px|various scales: lin-lin, lin-log, log-lin, and [[log
Logarithmic_scales_of_measurement