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A logarithmic scale is a Scale Of Measurement that uses the Logarithm of a Physical Quantity instead of the quantity itself. Presentation of data on a logarithmic scale can be helpful when the data covers a large range of values; the logarithm reduces this to a more manageable range. Some of our Sense s operate in a logarithmic fashion (doubling the input strength adds a constant to the subjective signal strength), 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. Logarithmic scales are either defined for ''ratios'' of the underlying quantity, or one has to agree to measure the quantity in fixed units. Deviating from these units means that the logarithmic measure will change by an ''additive'' constant. The base of the logarithm also has to be specified, unless the scale's value is considered to be a dimensional quantity expressed in generic (indefinite-base) Logarithmic Units . On most logarithmic scales, ''small'' values (or ratios) of the underlying quantity correspond to ''small'' (possibly negative) values of the logarithmic measure. Well-known examples of such scales are:
Some logarithmic scales were designed such that ''large'' values (or ratios) of the underlying quantity correspond to ''small'' values of the logarithmic measure. Examples of such scales are:
GRAPHIC REPRESENTATION A logarithmic scale is also a graphic scale on one or both sides of a graph where a number ''x'' is printed at a distance ''c''ยท10^log(''x'') from the point marked with the number 1. A Slide Rule has logarithmic scales, and Nomogram s often employ logarithmic scales. On a logarithmic scale an equal difference in Order Of Magnitude is represented by an equal distance. The Geometric Mean of two numbers is midway between the numbers. Logarithmic graph paper, before the advent of computer graphics, was a basic scientific tool. Plots on paper with one log scale can show up Exponential Law s, and on log-log paper Power Law s, as straight lines. SEE ALSO |
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