Question Number 149271 by Samimsultani last updated on 04/Aug/21
Answered by fred last updated on 04/Aug/21
$${x}^{{x}^{\mathrm{4}} } =\mathrm{4} \\ $$$${x}=\mathrm{4}^{\frac{\mathrm{1}}{\mathrm{4}}} \\ $$
Answered by nimnim last updated on 04/Aug/21
$$\Rightarrow\sqrt[{\frac{\mathrm{1}}{{x}}}]{\left(\left({x}^{{x}} \right)^{{x}} \right)^{{x}} }=\mathrm{4}\:\:\:\:\Rightarrow\left({x}^{{x}^{\mathrm{3}} } \right)^{{x}} =\mathrm{4}\:\:\:\:\Rightarrow{x}^{{x}^{\mathrm{4}} } =\mathrm{4} \\ $$$$\Rightarrow\:{x}^{{x}^{\mathrm{4}} } =\left(\sqrt{\mathrm{2}}\right)^{\left(\sqrt{\mathrm{2}}\right)^{\mathrm{4}} } \Rightarrow\:{x}=\sqrt{\mathrm{2}}\:\bigstar \\ $$