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受欢迎的代数 >

2^x=|31x-85|

解答

2^{x} = ∣ 31 x - 85 ∣

解答

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 )}

+1

十进制

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

求解步骤

2^{x} = ∣ 31 x - 85 ∣

找到正负区间

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

对每个区间解不等式

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 )}

作图

流行的例子

- 8 = 8 ∣ h ∣

∣ j ∣ + 1 = 15

2 ∣ y - 8 ∣ + 10 = 30

∣ 5 x - 4 ∣ = 10

6 ∣ c ∣ = 0