logarithmic

Log·a·rith·mic·al , a.

[Cf. F. logarithmique.]

1. Of or pertaining to logarithms; consisting of logarithms.

2. Using logarithms; as, logarithmic graph paper; a logarithmic scale.
[PJC]

3. Having a logarithm in one or more of the unknowns; -- of an equation.
[PJC]

Logarithmic curve (Math.), a curve which, referred to a system of rectangular coördinate axes, is such that the ordinate of any point will be the logarithm of its abscissa. -- Logarithmic spiral, a spiral curve such that radii drawn from its pole or eye at equal angles with each other are in continual proportion. See Spiral.

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[Etymology: from logarithm] mathematics A logarithmic scale has member values corresponding with the logarithm of the values of the measured entity; it is synonymously a geometric scale.

The term logarithmic scale applied to the axis of a graph indicates that equal-length steps along it represent recurrent multiplication of the actual variable by a constant amount (of value depending on the size of the steps). If that axis is for observed values and the other axis is linear, then it represents a geometric measurement scale for the observed variable. If both axes are logarithmic (as on ‘log-log’ paper), then, if the fundamental variables are x and y, the graphical relationship is between log x and log y, e.g. if linear

a·log x = c + b·log y, i.e. log x^a = c + log y^b

for some values a, b, and c; hence, assuming common logs,

x^a = 10^c·y^b.