Question Number 196098 by sonukgindia last updated on 18/Aug/23
Answered by mr W last updated on 18/Aug/23
$${x}^{\frac{\mathrm{1}}{\mathrm{2}^{{x}^{\mathrm{4}} } }} ={x}^{\frac{\mathrm{1}}{\mathrm{4}^{{x}^{\mathrm{2}} } }} \\ $$$$\Rightarrow{x}=\mathrm{0} \\ $$$$\Rightarrow{x}=\mathrm{1} \\ $$$$\Rightarrow\mathrm{2}^{{x}^{\mathrm{4}} } =\mathrm{4}^{{x}^{\mathrm{2}{x}} } \:\Rightarrow{x}^{\mathrm{4}} =\mathrm{2}{x}^{\mathrm{2}} \:\Rightarrow\left({x}^{\mathrm{2}} \right)^{\mathrm{2}} =\mathrm{2}{x}^{\mathrm{2}} \\ $$$$\Rightarrow{x}^{\mathrm{2}} =\mathrm{0}\:{or}\:{x}^{\mathrm{2}} =\mathrm{2}\:\Rightarrow{x}=\sqrt{\mathrm{2}} \\ $$