10.2^{x^2-4}=320

解

10. 2^{x^{2} - 4} = 320

x = \frac{ln ( 320 )}{ln ( 10.2 )} + 4, x = - \frac{ln ( 320 )}{ln ( 10.2 )} + 4

十進法表記

x = 2.54632 \dots, x = - 2.54632 \dots

解答ステップ

10. 2^{x^{2} - 4} = 320

指数の規則を適用する

(x^{2} - 4) ln (10.2) = ln (320)

解く

(x^{2} - 4) ln (10.2) = ln (320) : x = \frac{ln ( 320 )}{ln ( 10.2 )} + 4, x = - \frac{ln ( 320 )}{ln ( 10.2 )} + 4

x = \frac{ln ( 320 )}{ln ( 10.2 )} + 4, x = - \frac{ln ( 320 )}{ln ( 10.2 )} + 4