Origin of logarithmic sense responses?
First, the curves are not really logarithmic. 

Instead, according to the Stevens' power law, the curves are of the form: 

Perceived = k (actual)a 

where "a" could be greater, less than, or equal to 1.  

When "a" is 1, the curve is linear.  

Examples of a=1 (linear), are: 

brightness of a "point source briefly flashed"
length perception
cold perception of skin
radiant heat perception 

If "a" = 0.5, the curve is a square root curve.  Brightness perception follows the square root (or de Vries-Rose) curve in some intensity regions, and a nearly-linear response in other (Weber's law) regions.  

Examples of "a" being positive are perception of electric shock and perception of heaviness of lifted weights.  

So, since the perception curves can be linear (a=1), more sensitive than linear (a>1), or less sensitive than linear (a&lt;1), there is no general logarithmic property of neutrons that is responsible for the curves.