Log scales are used because of the very long range of
film. Density is proportional to exposure for pictorial
films. Some other films, notably lithographic films, have a
very sharp threshold between a developable exposure and one
that is not so that the density goes from minimum to maximum
for a very small difference in exposure.
  The scale of the film (or paper) depends on the
distribution of sensitivity of the silver halide crystals.
Each crystal has a threshold below which it is not
developable and above which it is. The gray values depend on
the number of developed crystals in a given area. By
controlling the range of sensitivities of the crystals in
the emulsion the contrast of the emulsion can be varied over
a very wide range. This distribution is controlled by the
exact method by which the emulsion is made, the rate of
solution of the components of the halide, nature of the
gelatin, additives, etc. Also, emulsions are often made from
two or more components and many pictorial films have
multiple coatings of emulsions of differing characteristics.
  Since a pictorial scene may have a brightness ratio of
1000:1 or more, and since the density range ratio is around
1:20 log scales are convenient.

Film is fundamentally non-linear. The curve in the
example provided above is simply a Tmax curve. An
inherent characteristic of Tmax is that it exhibits
a very long straight line section above the toe and
never really shoulders off. Other films exhibit
different curves depending on the emulsion.

Likewise, different papers will exhibit different paper
curves...