\sqrt[x]{x}=sqrt(0.5)

解

x x = 0.5

x = - \frac{2 W _{0} ( - \frac{l n ( 0.5 )}{2} )}{ln ( 0.5 )}

十進法表記

x = 0.76666 \dots

解答ステップ

x x = 0.5

指数の規則を適用する

\frac{1}{x} ln (x) = \frac{1}{2} ln (0.5)

解く

\frac{1}{x} ln (x) = \frac{1}{2} ln (0.5) : x = - \frac{2 W _{0} ( - \frac{l n ( 0.5 )}{2} )}{ln ( 0.5 )}

x = - \frac{2 W _{0} ( - \frac{l n ( 0.5 )}{2} )}{ln ( 0.5 )}