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Question Number 196098 by sonukgindia last updated on 18/Aug/23

Answered by mr W last updated on 18/Aug/23

x^(1/2^x^4  ) =x^(1/4^x^2  )   ⇒x=0  ⇒x=1  ⇒2^x^4  =4^x^(2x)   ⇒x^4 =2x^2  ⇒(x^2 )^2 =2x^2   ⇒x^2 =0 or x^2 =2 ⇒x=(√2)

$${x}^{\frac{\mathrm{1}}{\mathrm{2}^{{x}^{\mathrm{4}} } }} ={x}^{\frac{\mathrm{1}}{\mathrm{4}^{{x}^{\mathrm{2}} } }} \\ $$$$\Rightarrow{x}=\mathrm{0} \\ $$$$\Rightarrow{x}=\mathrm{1} \\ $$$$\Rightarrow\mathrm{2}^{{x}^{\mathrm{4}} } =\mathrm{4}^{{x}^{\mathrm{2}{x}} } \:\Rightarrow{x}^{\mathrm{4}} =\mathrm{2}{x}^{\mathrm{2}} \:\Rightarrow\left({x}^{\mathrm{2}} \right)^{\mathrm{2}} =\mathrm{2}{x}^{\mathrm{2}} \\ $$$$\Rightarrow{x}^{\mathrm{2}} =\mathrm{0}\:{or}\:{x}^{\mathrm{2}} =\mathrm{2}\:\Rightarrow{x}=\sqrt{\mathrm{2}} \\ $$

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