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Question-200110




Question Number 200110 by sonukgindia last updated on 14/Nov/23
Answered by mr W last updated on 14/Nov/23
x^x^x  =x^3   ⇒x=±1  ⇒x^x =3⇒e^(ln x) ln x=ln 3 ⇒x=((ln 3)/(W(ln 3)))≈1.825455
$${x}^{{x}^{{x}} } ={x}^{\mathrm{3}} \\ $$$$\Rightarrow{x}=\pm\mathrm{1} \\ $$$$\Rightarrow{x}^{{x}} =\mathrm{3}\Rightarrow{e}^{\mathrm{ln}\:{x}} \mathrm{ln}\:{x}=\mathrm{ln}\:\mathrm{3}\:\Rightarrow{x}=\frac{\mathrm{ln}\:\mathrm{3}}{{W}\left(\mathrm{ln}\:\mathrm{3}\right)}\approx\mathrm{1}.\mathrm{825455} \\ $$

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