page_title: Logarithmic scale
section_title: Common uses
hierarchical_section_title: Logarithmic scale / Common uses
caption_attribution_description: Number of deaths by country of citizenship as listed on the Wikipedia article Countries affected by the 2004 Indian Ocean earthquake on 3 December 2008, quantified through a logarithmic scale.
context_page_description: A logarithmic scale is a way of displaying numerical data over a very wide range of values in a compact way—typically the largest numbers in the data are hundreds or even thousands of times larger than the smallest numbers. Such a scale is nonlinear: the numbers 10 and 20, and 60 and 70, are not the same distance apart on a log scale. Rather, the numbers 10 and 100, and 60 and 600 are equally spaced. Thus moving a set distance along the scale means the number has been multiplied by 10. Often exponential growth curves are displayed on a log scale, otherwise they would increase too quickly to fit within a small graph. Another way to think about it is that the number of digits of the data grows at a constant rate. The numbers 10, 100, 1000, and 10000 are equally spaced on a log scale, but the number of digits is going up by 1 each time: 2, 3, 4, and 5 digits. In this way, adding two digits multiplies the quantity measured on the log scale by a factor of 100.
context_section_description: The markings on slide rules are arranged in a log scale for multiplying or dividing numbers by adding or subtracting lengths on the scales.
  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 
  Sound level, with units decibel
  Neper for amplitude, field and power quantities
  Frequency level, with units 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
  The rule of 'nines' used for rating low probabilities
  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
  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 (Weber–Fechner 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 in some cultures. It can also be used for geographical purposes, for instance for measuring the speed of earthquakes.
caption: A logarithmic scale makes it easy to compare values that cover a large range, such as in this map.
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