Question Number 10970 by Joel576 last updated on 04/Mar/17
$${x}^{{x}^{{x}^{\iddots^{\mathrm{2}} } } } \:=\:\mathrm{2} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}\:? \\ $$
Answered by ridwan balatif last updated on 04/Mar/17
$$\mathrm{we}\:\mathrm{know}\:\mathrm{x}^{\mathrm{x}^{\mathrm{x}^{\mathrm{x}^{.^{.^{...} \:} } \:} } } =\mathrm{2} \\ $$$$\mathrm{so}\:\mathrm{x}^{\left(\mathrm{x}^{\mathrm{x}^{\mathrm{x}^{\mathrm{x}^{.^{..} } } } } \right)} =\mathrm{2} \\ $$$$\mathrm{x}^{\mathrm{2}} =\mathrm{2} \\ $$$$\mathrm{x}=\sqrt{\mathrm{2}} \\ $$
Commented by Joel576 last updated on 05/Mar/17
$${thank}\:{you}\:{very}\:{much} \\ $$
Commented by Joel576 last updated on 05/Mar/17
$${thank}\:{you}\:{very}\:{much} \\ $$