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Question Number 10970 by Joel576 last updated on 04/Mar/17

x^x^x^⋰^2     = 2  What is the value of x ?

$${x}^{{x}^{{x}^{\iddots^{\mathrm{2}} } } } \:=\:\mathrm{2} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}\:? \\ $$

Answered by ridwan balatif last updated on 04/Mar/17

we know x^x^x^(x^.^(.^(...)  )   )   =2  so x^((x^x^x^x^.^(..)     )) =2  x^2 =2  x=(√2)

$$\mathrm{we}\:\mathrm{know}\:\mathrm{x}^{\mathrm{x}^{\mathrm{x}^{\mathrm{x}^{.^{.^{...} \:} } \:} } } =\mathrm{2} \\ $$$$\mathrm{so}\:\mathrm{x}^{\left(\mathrm{x}^{\mathrm{x}^{\mathrm{x}^{\mathrm{x}^{.^{..} } } } } \right)} =\mathrm{2} \\ $$$$\mathrm{x}^{\mathrm{2}} =\mathrm{2} \\ $$$$\mathrm{x}=\sqrt{\mathrm{2}} \\ $$

Commented by Joel576 last updated on 05/Mar/17

thank you very much

$${thank}\:{you}\:{very}\:{much} \\ $$

Commented by Joel576 last updated on 05/Mar/17

thank you very much

$${thank}\:{you}\:{very}\:{much} \\ $$

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