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In a recent work [JNT \textbf{129}, 2154 (2009)], Gun and co-workers haveclaimed that the number $\,\log{\Gamma(x)} + \log{\Gamma(1-x)}\,$, $x$ being arational number between $0$ and $1$, is transcendental with at most \emph{one}possible exception, but the proof presented there in that work is\emph{incorrect}. Here in this paper, I point out the mistake they committedand I present a theorem that establishes the transcendence of those numberswith at most \emph{two} possible exceptions. As a consequence, I make use ofthe reflection property of this function to establish a criteria for thetranscendence of $\,\log{\pi}$, a number whose irrationality is not proved yet.This has an interesting consequence for the transcendence of the product $\,\pi\cdot e$, another number whose irrationality remains unproven.

On the possible exceptions for the transcendence of the log-gamma function at rational entries