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Question Number 199103 by tri26112004 last updated on 28/Oct/23

Commented by mr W last updated on 28/Oct/23

(4)^(1/x) =x  4^(1/x) =x  2^(2/x) =x  ⇒x=2

$$\sqrt[{{x}}]{\mathrm{4}}={x} \\ $$$$\mathrm{4}^{\frac{\mathrm{1}}{{x}}} ={x} \\ $$$$\mathrm{2}^{\frac{\mathrm{2}}{{x}}} ={x} \\ $$$$\Rightarrow{x}=\mathrm{2} \\ $$

Commented by mr W last updated on 28/Oct/23

more interesting is to find       (5)^(1/(...))            (√5)                (√5)  = ?

$${more}\:{interesting}\:{is}\:{to}\:{find} \\ $$$$\:\:\:\:\:\sqrt[{...}]{\mathrm{5}} \\ $$$$\:\:\:\:\:\:\:\:\:\sqrt{\mathrm{5}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\sqrt{\mathrm{5}}\:\:=\:? \\ $$

Answered by deleteduser1 last updated on 28/Oct/23

(4)^(1/(4)^(1/(...(√4))) ) =(4)^(1/(√4)) =(√4)=2

$$\sqrt[{\sqrt[{...\sqrt{\mathrm{4}}}]{\mathrm{4}}}]{\mathrm{4}}=\sqrt[{\sqrt{\mathrm{4}}}]{\mathrm{4}}=\sqrt{\mathrm{4}}=\mathrm{2} \\ $$

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