5^{x^2}=17

解

5^{x^{2}} = 17

x = \frac{ln ( 17 )}{ln ( 5 )}, x = - \frac{ln ( 17 )}{ln ( 5 )}

十進法表記

x = 1.32679 \dots, x = - 1.32679 \dots

解答ステップ

5^{x^{2}} = 17

指数の規則を適用する

x^{2} ln (5) = ln (17)

解く

x^{2} ln (5) = ln (17) : x = \frac{ln ( 17 )}{ln ( 5 )}, x = - \frac{ln ( 17 )}{ln ( 5 )}

x = \frac{ln ( 17 )}{ln ( 5 )}, x = - \frac{ln ( 17 )}{ln ( 5 )}