  Quantum effects due to conformal matter in a black hole background result in
universal logarithmic corrections to black-hole entropy. The universality
resides in the connection of the log term coefficient with those of type-A and
type-B Weyl anomalies, regularization-scheme independent quantities. We
presently study the case of extremal black holes within Wald's Noether charge
formalism. In the conformal class of flat metrics, we are again able to unveil
the log term in the entropy from the horizon value of the solution to the
Q-curvature uniformization problem. Beyond conformally flat backgrounds, type-B
Weyl anomaly becomes an obstruction to considering flat space as the fiducial
metric and the search for a metric of constant Q-curvature remains open.
Notwithstanding, by a uniform scaling argument we show that the results based
on heat kernel and euclidean computations (namely entropy function and conical
defect) can also be derived as Wald entropy, that is, as Noether charge of the
integrated anomaly or conformal index. We finally comment on the relation with
entanglement entropy.
