  We analyze large logarithmic corrections to 4D black hole entropy and relate
them to the Weyl anomaly. We use duality to show that counter-terms in
Einstein-Maxwell theory can be expressed in terms of geometry alone, with no
dependence on matter terms. We analyze the two known $\mathcal{N} = 2$
supersymmetric invariants for various non-supersymmetric black holes and find
that both reduce to the Euler invariant. The $c$-anomaly therefore vanishes in
these theories and the coefficient of the large logarithms becomes topological.
It is therefore independent of continuous black hole parameters, such as the
mass, even far from extremality.
