What is Logarithmic scale?
[[File:COB data Tsunami deaths.PNG|thumb|400px|right|A log scale makes it easy to compare values that cover a large range, such as in this map]] A '''logarithmic scale''' is a [[scale (measurement)|scale]] used when there is a large range of quantities. Common uses include [[Richter magnitude scale|earthquake strength]], [[acoustics|sound loudness]], [[optics|light intensity]], spreading rates of [[epidemics]], and [[PH|pH of solutions]]. It is based on [[orders of magnitude]], rather than a standard [[linear scale]]. The value of each mark on the scale is the value at the previous mark multiplied by a constant. Logarithmic scales are also used in [[slide rule]]s for multiplying or dividing numbers by adding or subtracting lengths on the scales. [[File:slide rule example3.svg|thumb|center|The two logarithmic scales of a slide rule]] The logarithmic scale can be helpful when the data cover a large range of values – the logarithm reduces this to a more manageable range. Some of our [[sense]]s operate in a logarithmic fashion (multiplying the actual input strength adds a constant to the perceived signal strength, see: [[Stevens' power law]]). That makes logarithmic scales for these input quantities especially appropriate. In particular, our sense of [[hearing]] [[perception|perceives]] equal ''multiples'' of [[frequency|frequencies]] as equal ''differences'' in pitch. On most logarithmic scales, ''small'' multiples (or ratios) of the underlying quantity correspond to ''small'' (possibly negative) values of the logarithmic measure. == Examples == Well-known examples of such scales are: * [[Richter magnitude scale]] and [[moment magnitude scale]] (MMS) for strength of [[earthquakes]] and [[Motion (physics)|movement]] in the [[earth]]. * [[decibel|bel and decibel]] and [[neper]] for acoustic power (loudness) and electric power; * counting [[f-stop]]s for ratios of [[photographic exposure]]; * rating low [[probabilities]] by the number of 'nines' in the decimal expansion of the probability of their not happen