  Using the Wald's relation between the Noether charge of diffeomorphisms and
the entropy for a generic spacetime possessing a bifurcation surface, we
introduce a method to obtain a family of higher order derivatives effective
actions from the entropy of black holes. Our point of view is to consider
fundamental the black hole entropy and the action an emerged object. We then
specialize to a particular class of effective theories: the f(R) theories. We
apply the idea, using a simple mind ansatz, to loop quantum gravity and to a
general class of log-corrected entropy formulas.
