  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.
