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We examine the logarithmic corrections to the black hole (BH) entropy productformula of outer horizon and inner horizon by taking into account the\emph{effects of statistical quantum fluctuations around the thermalequilibrium} and \emph{via conformal field theory} (CFT). We argue thatlogarithmic corrections to the BH entropy product formula when calculated usingCFT and taking into the effects of quantum fluctuations around the thermalequilibrium, the formula should \emph{not be universal} and it should also\emph{not be quantized}. These results have been explicitly checked by givingseveral examples.

CFT and Logarithmic Corrections to the Black Hole Entropy Product Formula