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受欢迎的代数 >

2^x+x=5

解答

2^{x} + x = 5

解答

x = - \frac{W _{0} ( 32 ln ( 2 ) ) - 5 ln ( 2 )}{ln ( 2 )}

+1

十进制

x = 1.71562 \dots

求解步骤

2^{x} + x = 5

将

2^{x} + x = 5

调整为朗伯形式:

1 = (5 - x) e^{- l n (2) x}

用

(- x + 5) ln (2) = u

和

x = - \frac{u - 5 ln ( 2 )}{ln ( 2 )}

改写方程式

1 = (5 - (- \frac{u - 5 ln ( 2 )}{ln ( 2 )})) e^{- l n (2) (- \frac{u - 5 l n ( 2 )}{l n ( 2 )})}

化简

1 = e^{u - 5 l n (2)} (5 + \frac{u - 5 ln ( 2 )}{ln ( 2 )})

改写

1 = e^{u - 5 l n (2)} (5 + \frac{u - 5 ln ( 2 )}{ln ( 2 )})

为朗伯形式:

e^{u} u = 32 ln (2)

解

e^{u} u = 32 ln (2) : u = W_{0} (32 ln (2))

u = W_{0} (32 ln (2))

代回

u = (- x + 5) ln (2)

，求解

x

解

(- x + 5) ln (2) = W_{0} (32 ln (2)) : x = - \frac{W _{0} ( 32 ln ( 2 ) ) - 5 ln ( 2 )}{ln ( 2 )}

x = - \frac{W _{0} ( 32 ln ( 2 ) ) - 5 ln ( 2 )}{ln ( 2 )}

作图

流行的例子

9^{x+2}=27^{-x}

9^{x + 2} = 2 7^{- x}

-24× 3^{x-1}+9^x=9

- 24 \times 3^{x - 1} + 9^{x} = 9

7^{- x} = 49

6=34.416e^{-0.18(t)}

6 = 34.416 e^{- 0.18 (t)}

(1+x^2)2^x-5*2^x=0

(1 + x^{2}) 2^{x} - 5 \cdot 2^{x} = 0