  The electric and magnetic black hole solutions are found by coupling the
recently introduced nonlinear electrodynamics (NED) model, called "double
logharitmic nonlinear electrodynamics" with cosmological Einstein gravity. The
solutions become Reissner-Nordstrom (RN) black hole in the weak field limit and
asymptotically. The electric solution is expressed as an integral equation
while the magnetic black hole solution is expressed in terms of elementary
functions. Hence, the thermodynamic structure of the magnetic black hole
solution is analyzed by deriving the modified Smarr's formula and studying the
first law of thermodynamics. Moreover, its stability is investigated by
deriving the heat capacity.
