Chapter 5.3, Problem 94E

Perception. The Weber–Fechner law concerns a person’s sensed perception of various strengths of stimulation involving weights, sound, light, shock, taste, and so on. One form of the law states that the rate of change of sensed sensation S with respect to stimulus R is inversely proportional to the strength of the stimulus R. So

     $\frac{ds}{dR}=\frac{k}{R}$

where k is a constant. If we let R₀ be the threshold level at which the stimulus R can be detected (the least amount of sound, light, weight, and so on, that can be detected), then

     $S(R_0)=0$

Find a function S in terms of R that satisfies these conditions.