In my question Question I have discussed in the comments of the domain of $$(\log{x})^{-e^x}$$ In wolfram alpha as matter of fact the domain is $x\geq 1$, but I am not convinced of this fact since when I have $x=1$ it appears $0$ at the denominator, for the reason why $(\log{x})^{-e^x}=\frac{1}{(\log{x})^{e^x}}$.
Can you help me in understanding why in WA I have this kind of strange answer?