Motivated by the string theory corrections in the low-energy limit of both gauge and gravity sides, we
consider three-dimensional black holes in the presence of dilatonic gravity and the Born-Infeld nonlinear
electromagnetic field. We find that geometric behavior of the solutions is similar to the behavior of the
hyperscaling violation metric, asymptotically. We also investigate thermodynamics of the solutions and
show that the generalization to dilatonic gravity introduces novel properties into thermodynamics of the
black holes which were absent in the Einstein gravity. Furthermore, we explore the possibility of tuning out
part of the dilatonic effects using the Born-Infeld generalization.
