  We propose a model describing Einstein gravity coupled to a scalar field with
an exponential potential. We show that the weak-field limit of the model has
static solutions given by a gravitational potential behaving for large
distances as \ln r . The Newtonian term GM/r appears only as subleading. Our
model can be used to give a phenomenological explanation of the rotation curves
of the galaxies without postulating the presence of dark matter. This can be
achieved only by giving up at galactic scales Einstein equivalence principle.
