  In contrast to its chargeless version the charged Banados, Taitelboim and
Zanelli (BTZ) metric in linear Maxwell electromagnetism is known to be singular
at r=0. We show, by employing nonlinear electrodynamics that one obtains
charged, extension of the BTZ metric with regular electric field. This we do by
choosing a logarithmic Lagrangian for the nonlinear electrodynamics. A Theorem
is proved on the existence of electric black holes and combining this results
with a duality principle disproves the existence of magnetic black holes in
2+1-dimensions.
