Question Number 128508 by Lian last updated on 08/Jan/21
$${if}\:\:{x}^{{x}^{\mathrm{3}} } =\mathrm{3} \\ $$$${find}\:{x} \\ $$
Answered by mr W last updated on 08/Jan/21
$${if}\:{x}^{\mathrm{3}} =\mathrm{3},\:{x}^{{x}^{\mathrm{3}} } ={x}^{\mathrm{3}} =\mathrm{3} \\ $$$${that}\:{means}\:{x}^{{x}^{\mathrm{3}} } =\mathrm{3}\:\Leftrightarrow\:{x}^{\mathrm{3}} =\mathrm{3} \\ $$$$\Rightarrow{x}=\sqrt[{\mathrm{3}}]{\mathrm{3}} \\ $$$$ \\ $$$${generally}\:{for}\:{any}\:{number}\:{of}\:{times}\:{x} \\ $$$${x}^{{x}^{......{x}^{{a}} } } ={a}>\mathrm{0}\:\Rightarrow{x}=\sqrt[{{a}}]{{a}} \\ $$
Commented by Lian last updated on 08/Jan/21
$${nice} \\ $$