On the Existence of the Logarithmic Correction Term in Black Hole   Entropy-Area Relation
  In this paper we consider a model universe with large extra dimensions to obtain a modified black hole entropy-area relation. We use the generalized uncertainty principle to find a relation between the number of spacetime dimensions and the presence or vanishing of logarithmic prefactor in the black hole entropy-area relation. Our calculations are restricted to the microcanonical ensembles and we show that in the modified entropy-area relation, the microcanonical logarithmic prefactor appears only when spacetime has an even number of dimensions. 
Kourosh Nozari and A. S. Sefiedgar