  A simple regular black hole solution satisfying the weak energy condition is
obtained within Einstein--non--linear electrodynamics theory. We have computed
the thermodynamic properties of this black hole by a careful analysis of the
horizons and we have found that the usual Bekenstein--Hawking entropy gets
corrected by a logarithmic term. Therefore, in this sense our model realizes
some quantum gravity predictions which add this kind of correction to the black
hole entropy. In particular, we have established some similitudes between our
model and a quadratic generalized uncertainty principle. This similitude has
been confirmed by the existence of a remnant, which prevents complete
evaporation, in agreement with the quadratic generalized uncertainty principle
case.
