2^x=|31x-85|

Lösung

2^{x} = ∣ 31 x - 85 ∣

x = - \frac{31 W _{0} ( \frac{e ^{\frac{85 l n ( 2 )}{31}} l n ( 2 )}{31} ) - 85 ln ( 2 )}{31 ln ( 2 )} or x = - \frac{31 W _{0} ( - \frac{e ^{\frac{85 l n ( 2 )}{31}} l n ( 2 )}{31} ) - 85 ln ( 2 )}{31 ln ( 2 )} or x = - \frac{31 W _{- 1} ( - \frac{e ^{\frac{85 l n ( 2 )}{31}} l n ( 2 )}{31} ) - 85 ln ( 2 )}{31 ln ( 2 )}

Dezimale

x = 2.55267 \dots, x = 3, x = 7.06687 \dots

Schritte zur Lösung

2^{x} = ∣ 31 x - 85 ∣

Finde positive und negative Intervalle

x < \frac{85}{31}, x \geq \frac{85}{31}

Löse die Ungleichung für jedes Intervall

x = - \frac{31 W _{0} ( \frac{e ^{\frac{85 l n ( 2 )}{31}} l n ( 2 )}{31} ) - 85 ln ( 2 )}{31 ln ( 2 )} or x = - \frac{31 W _{0} ( - \frac{e ^{\frac{85 l n ( 2 )}{31}} l n ( 2 )}{31} ) - 85 ln ( 2 )}{31 ln ( 2 )} or x = - \frac{31 W _{- 1} ( - \frac{e ^{\frac{85 l n ( 2 )}{31}} l n ( 2 )}{31} ) - 85 ln ( 2 )}{31 ln ( 2 )}

x = - \frac{31 W _{0} ( \frac{e ^{\frac{85 l n ( 2 )}{31}} l n ( 2 )}{31} ) - 85 ln ( 2 )}{31 ln ( 2 )} or x = - \frac{31 W _{0} ( - \frac{e ^{\frac{85 l n ( 2 )}{31}} l n ( 2 )}{31} ) - 85 ln ( 2 )}{31 ln ( 2 )} or x = - \frac{31 W _{- 1} ( - \frac{e ^{\frac{85 l n ( 2 )}{31}} l n ( 2 )}{31} ) - 85 ln ( 2 )}{31 ln ( 2 )}

- 8 = 8 ∣ h ∣

∣ j ∣ + 1 = 15

2 ∣ y - 8 ∣ + 10 = 30

∣ 5 x - 4 ∣ = 10

6 ∣ c ∣ = 0