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Concept
Logarithmic scale
Summary
A logarithmic scale (or log scale) is a way of displaying numerical data over a very wide range of values in a compact way. As opposed to a linear number line in which every unit of distance corresponds to adding by the same amount, on a logarithmic scale, every unit of length corresponds to multiplying the previous value by the same amount. Hence, such a scale is nonlinear: the numbers 1, 2, 3, 4, 5, and so on, are not equally spaced. Rather, the numbers 10, 100, 1000, 10000, and 100000 would be equally spaced. Likewise, the numbers 2, 4, 8, 16, 32, and so on, would be equally spaced. Often exponential growth curves are displayed on a log scale, otherwise they would increase too quickly to fit within a small graph.
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.
Official source
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