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受欢迎的代数 >

2^2x-6.2^x+8=0

解答

2^{2} x - 6. 2^{x} + 8 = 0

解答

x = - \frac{W _{- 1} ( - \frac{l n ( 6.2 )}{153.76} ) + 2 ln ( 6.2 )}{ln ( 6.2 )}, x = - \frac{W _{0} ( - \frac{l n ( 6.2 )}{153.76} ) + 2 ln ( 6.2 )}{ln ( 6.2 )}

+1

十进制

x = 1.43635 \dots, x = - 1.99341 \dots

求解步骤

2^{2} x - 6. 2^{x} + 8 = 0

将

2^{2} x - 6. 2^{x} + 8 = 0

调整为朗伯形式:

- 1 = - e^{- l n (6.2) x} (4 x + 8)

用

(- x - 2) ln (6.2) = u

和

x = - \frac{u + 2 ln ( 6.2 )}{ln ( 6.2 )}

改写方程式

- 1 = - e^{- l n (6.2) (- \frac{u + 2 l n ( 6.2 )}{l n ( 6.2 )})} (4 (- \frac{u + 2 ln ( 6.2 )}{ln ( 6.2 )}) + 8)

化简

- 1 = - e^{u + 2 l n (6.2)} (- \frac{4 ( u + 2 ln ( 6.2 ) )}{ln ( 6.2 )} + 8)

改写

- 1 = - e^{u + 2 l n (6.2)} (- \frac{4 ( u + 2 ln ( 6.2 ) )}{ln ( 6.2 )} + 8)

为朗伯形式:

e^{u} u = - \frac{ln ( 6.2 )}{153.76}

解

e^{u} u = - \frac{ln ( 6.2 )}{153.76} : u = W_{- 1} (- \frac{ln ( 6.2 )}{153.76}), u = W_{0} (- \frac{ln ( 6.2 )}{153.76})

u = W_{- 1} (- \frac{ln ( 6.2 )}{153.76}), u = W_{0} (- \frac{ln ( 6.2 )}{153.76})

代回

u = (- x - 2) ln (6.2)

，求解

x

解

(- x - 2) ln (6.2) = W_{- 1} (- \frac{ln ( 6.2 )}{153.76}) : x = - \frac{W _{- 1} ( - \frac{l n ( 6.2 )}{153.76} ) + 2 ln ( 6.2 )}{ln ( 6.2 )}

解

(- x - 2) ln (6.2) = W_{0} (- \frac{ln ( 6.2 )}{153.76}) : x = - \frac{W _{0} ( - \frac{l n ( 6.2 )}{153.76} ) + 2 ln ( 6.2 )}{ln ( 6.2 )}

x = - \frac{W _{- 1} ( - \frac{l n ( 6.2 )}{153.76} ) + 2 ln ( 6.2 )}{ln ( 6.2 )}, x = - \frac{W _{0} ( - \frac{l n ( 6.2 )}{153.76} ) + 2 ln ( 6.2 )}{ln ( 6.2 )}

作图

流行的例子

e^{9 x} = 9 e^{- x}

20 e^{7 k} = 60

45=8(4)^{0.99x}-19

45 = 8 (4)^{0.99 x} - 19

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solvefor x,be^{-2x}+3y+3x+11=0

so l v e f or x, b e^{- 2 x} + 3 y + 3 x + 11 = 0