Question Number 157832 by mathlove last updated on 28/Oct/21
Answered by mr W last updated on 28/Oct/21
$${x}^{{x}^{\frac{\mathrm{3}}{\mathrm{2}}} } ={x}^{{x}} {x}^{\frac{{x}}{\mathrm{2}}} \\ $$$${x}^{{x}^{\frac{\mathrm{3}}{\mathrm{2}}} −\frac{\mathrm{3}{x}}{\mathrm{2}}} =\mathrm{1} \\ $$$$\Rightarrow{x}=\mathrm{1} \\ $$$${or} \\ $$$$\Rightarrow{x}^{\frac{\mathrm{3}}{\mathrm{2}}} −\frac{\mathrm{3}{x}}{\mathrm{2}}=\mathrm{0} \\ $$$$\Rightarrow{x}^{\frac{\mathrm{3}}{\mathrm{2}}} =\frac{\mathrm{3}{x}}{\mathrm{2}} \\ $$$$\Rightarrow{x}^{\frac{\mathrm{3}}{\mathrm{2}}−\mathrm{1}} =\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\Rightarrow{x}^{\frac{\mathrm{1}}{\mathrm{2}}} =\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\Rightarrow{x}=\frac{\mathrm{9}}{\mathrm{4}} \\ $$$${summary}: \\ $$$${x}=\mathrm{1},\:\frac{\mathrm{9}}{\mathrm{4}} \\ $$
Commented by otchereabdullai@gmail.com last updated on 29/Oct/21
$$\mathrm{supper}\:\mathrm{prof} \\ $$
Commented by mathlove last updated on 30/Oct/21
$${thanks}\:{sir}\: \\ $$