  This work examines the magnetized black holes of Lovelock gravity in the
presence of double-logarithmic electrodynamics. In this context, the Lovelock
polynomial is found and the accompanying thermodynamic quantities, such as
mass, entropy, Hawking temperature, and heat capacity are determined. This new
model of nonlinear electrodynamics is used to calculate the black hole
solutions of Einstein, Gauss-Bonnet and third order Lovelock gravities as well.
The impacts of the double-logarithmic electromagnetic field on the black hole
thermodynamics in these particular theories are examined and the regions of
horizon radius that correspond to the local thermodynamic stability are
highlighted.
