The usefulness of logarithms in the measurement of many of the stimuli to which human beings are sensitive is almost too obvious to need argument. Three reasons are commonly given to justify the practice:
1. The intensity ranges of the physical stimuli are enormous—energy ranges of trillions to one are involved in vision and hearing.
2. To a rough approximation, discrimination follows a law of relativity: the just detectable increment in a stimulus is proportional to the magnitude of the stimulus (Weber's law). Hence, to the extent that Weber's law holds, the logarithmic difference that is just detectable is constant.
3. According to Fechner's law, the subjective magnitude of a sensation is supposed to be proportional to the logarithm of the magnitude of the stimulus.