We examine the logarithmic corrections to the black hole (BH) entropy product formula of outer horizon and inner horizon by taking into account the \emph{ effects of statistical quantum fluctuations around the thermal equilibrium} and \emph{ via conformal field theory} (CFT). We argue that logarithmic corrections to the BH entropy product formula when calculated using CFT and taking into the effects of quantum fluctuations around the thermal equilibrium, the formula should \emph{ not be universal} and it should also \emph{ not be quantized}. These results have been explicitly checked by giving several examples.
Categories: gr-qc hep-th