Question

$\large\bf\:if\:{x}^{x^{x}}= ({\dfrac{1}{2}})^{ \sqrt{2}}.\\\bf \: find \: x \: = \: ?$
Maths aryabhatta and genius solve this . ​

Answer 1

Answer:

$x \: = \: \frac{1}{2} \times \frac{1}{2}$

$x \: = \: \frac{1}{4}$

=$\large\bf\:{x}^{x^{x}}$

= 1 by 4 × 1 by 4 × 1 by 4

$x\: = \frac{1}{64}$

HOPE IT HELPS YOU

Answer 2

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$\red\leadsto\footnotesize\:{x}^{x^{x}}= ({\dfrac{1}{2}})^{ \sqrt{2}} \\ \\ \bf \: solving \:RHS, \\ \\\red\leadsto\footnotesize\:({\frac{1}{2} })^{ \sqrt{2} } \\ \\ \red\leadsto\footnotesize \:({\frac{1}{2}})^{ \frac{2\sqrt{2} }{2}} \\ \\ \red\leadsto\footnotesize \:(({\frac{1}{2}})^{2})^{ \frac{1}{\sqrt{2}}} \\ \\ \red\leadsto\footnotesize \:({\frac{1}{4}})^{ \frac{1}{\sqrt{2}}} \\ \\ \red\leadsto\footnotesize \:({\frac{1}{4}})^{\frac{1}{\sqrt{2}}^{(\frac{4}{4})}} \\ \\ \red\leadsto\footnotesize \:({\frac{1}{4}})^{(\frac{1}{\sqrt{2}})^4{(\frac{1}{4})}}\\\\\red\leadsto\footnotesize \:({\frac{1}{4}})^{(\frac{1}{4})^{(\frac{1}{4})}} \\ \\ \bf \: comparing \: with \:LHS \: Now, we \: get, \\ \\\red\leadsto\footnotesize\:{x}^{x^{x}}=({\frac{1}{4}})^{(\frac{1}{4})^{(\frac{1}{4})}} \\ \\\red\leadsto \: \orange\therefore \boxed{\red{\bf\:x =\dfrac{1}{4}}}$

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