x-x-x-1-2-2-find-x-

Question Number 145256 by Gbenga last updated on 03/Jul/21

x^{x^{x}} = {(\frac{1}{2})}^{\sqrt{2}}

find x

Commented by justtry last updated on 04/Jul/21

i t h i n k t h e r e i s n o t x \in R t o f i n d i t .

Answered by mr W last updated on 04/Jul/21

{(\frac{1}{2})}^{\sqrt{2}}

= {(\frac{1}{4})}^{\frac{\sqrt{2}}{2}}

= {(\frac{1}{4})}^{2^{- \frac{1}{2}}}

= {(\frac{1}{4})}^{4^{- \frac{1}{4}}}

= {(\frac{1}{4})}^{{(\frac{1}{4})}^{\frac{1}{4}}}

x^{x^{x}} = {(\frac{1}{4})}^{{(\frac{1}{4})}^{\frac{1}{4}}}

\Rightarrow x = \frac{1}{4}

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