let-x-x-x-2-x-2-2-x-2-then-let-x-x-x-4-x-4-4-x-4-1-4-2-so-we-had-prove-2-4-right-

Question Number 86298 by 21042009 last updated on 28/Mar/20

$${let}\:{x}^{{x}^{{x}^{\iddots} } } =\mathrm{2} \\ $$$${x}^{\mathrm{2}} =\mathrm{2} \\ $$$${x}=\pm\sqrt{\mathrm{2}} \\ $$$${then}\:{let}\:{x}^{{x}^{{x}^{\iddots} } } =\mathrm{4} \\ $$$${x}^{\mathrm{4}} =\mathrm{4} \\ $$$${x}=\pm\sqrt[{\mathrm{4}}]{\mathrm{4}}=\pm\sqrt{\mathrm{2}} \\ $$$${so}\:{we}\:{had}\:{prove}\:\mathrm{2}=\mathrm{4}\:{right}? \\ $$

Commented by john santu last updated on 28/Mar/20

$${hahaha}..{no} \\ $$

Commented by 20092104 last updated on 28/Mar/20

$${why} \\ $$

Commented by Kunal12588 last updated on 28/Mar/20

$$\mathrm{1}^{\mathrm{0}} =\mathrm{1},\:\mathrm{2}^{\mathrm{0}} =\mathrm{1} \\ $$$$\left.\mathrm{1}\neq\mathrm{2}\:\left({why}?\right)\::\right) \\ $$

Commented by john santu last updated on 28/Mar/20

$$\mathrm{10000000}^{\mathrm{0}} \:=\:\mathrm{e}^{\mathrm{0}} \\ $$$$\mathrm{10000000}\:=\:\mathrm{e}\: \\ $$$$\mathrm{why}? \\ $$

Commented by 20092104 last updated on 29/Mar/20

$${domain}\:{of}\:{x}^{{x}^{{x}^{\iddots} } } \:{is}\:\left[\frac{\mathrm{1}}{{e}^{{e}} },\:{e}^{\frac{\mathrm{1}}{{e}}} \right] \\ $$

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