Logarithmic units
A logarithmic unit is an abstract mathematical unit that can be used to express any quantity (physical or mathematical) that is defined on a logarithmic scale, that is, as being proportional to the value of a logarithm function. Here, a given logarithmic unit will be denoted using the notation [log n], where n is a positive real number, and [log ] here denotes the indefinite logarithm function .
Examples of logarithmic units include common units of information and entropy, such as the bit [log 2] and the byte 8[log 2] = [log 256], also the nat [log e] and the ban [log 10]; units of relative signal strength magnitude such as the decibel 0.1[log 10] and bel [log 10], neper [log e], and other logarithmic-scale units such as the Richter magnitude scale point [log 10] or (more generally) the corresponding order-of-magnitude unit sometimes referred to as a factor of ten or decade (here meaning [log 10], not 10 years). Musical pitch intervals are also logarithmic units on a frequency scale, such as octave [log 2], semitone, cent, etc.
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