When two parameters are involved, the relationship between the stimuli and perception is the square of the logarithm.
The only difference is the exponent, and as a result the logarithm, are negative.
The magnitude of an earthquake is determined from the logarithm of the amplitude of waves recorded by seismographs.
British Dictionary definitions for logarithm
logarithm
/ˈlɒɡəˌrɪðəm/
noun
1.
the exponent indicating the power to which a fixed number, the base, must be raised to obtain a given number or variable. It is used esp to simplify multiplication and division: if ax = M, then the logarithm of M to the base a (written logaM) is xOften shortened to log See also common logarithm, natural logarithm
Word Origin
C17: from New Latin logarithmus, coined 1614 by John Napier, from Greek logos ratio, reckoning + arithmos number
1610s, Modern Latin logarithmus, coined by Scottish mathematician John Napier (1550-1617), literally "ratio-number," from Greek logos "proportion, ratio, word" (see logos) + arithmos "number" (see arithmetic).
(lô'gə-rĭ'əm) The power to which a base must be raised to produce a given number. For example, if the base is 10, then the logarithm of 1,000 (written log 1,000 or log_{10} 1,000) is 3 because 10^{3} = 1,000. See more at common logarithm, natural logarithm.