  We consider Einstein gravity with a negative cosmological constant endowed
with distinct matter sources. The different models analyzed here share the
following two properties: (i) they admit static symmetric solutions with planar
base manifold characterized by their mass and some additional Noetherian
charges, and (ii) the contribution of these latter in the metric has a slower
falloff to zero than the mass term, and this slowness is of logarithmic order.
Under these hypothesis, it is shown that, for suitable bounds between the mass
and the additional Noetherian charges, the solutions can represent black holes
with two horizons whose locations are given in term of the real branches of the
Lambert W functions. We present various examples of such black hole solutions
with electric, dyonic or axionic charges with AdS and Lifshitz asymptotics. As
an illustrative example, we construct a purely AdS magnetic black hole in five
dimensions with a matter source given by three different Maxwell invariants.
