Question Number 143042 by 0731619 last updated on 09/Jun/21
Answered by Dwaipayan Shikari last updated on 09/Jun/21
$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}{log}\left({x}\right)={x}−\mathrm{1} \\ $$$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}{log}\left({x}\right)\frac{{x}^{{x}^{{x}^{?...} } } }{{x}^{\mathrm{2}} −\mathrm{1}}=\frac{{x}−\mathrm{1}}{{x}^{\mathrm{2}} −\mathrm{1}}.{x}^{{x}^{{x}^{{x}^{{x}^{..} } } } } =\frac{{x}^{{x}^{{x}^{{x}^{{x}} } } } }{{x}+\mathrm{1}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$