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受欢迎的代数 >

1500=0.85^xx7600

解答

1500 = 0.8 5^{x} x 7600

解答

x = \frac{W _{- 1} ( \frac{15 l n ( 0.85 )}{76} )}{ln ( 0.85 )}, x = \frac{W _{0} ( \frac{15 l n ( 0.85 )}{76} )}{ln ( 0.85 )}

+1

十进制

x = 31.14258 \dots, x = 0.20402 \dots

求解步骤

1500 = 0.8 5^{x} x \cdot 7600

将

1500 = 0.8 5^{x} x 7600

调整为朗伯形式:

1500 = e^{l n (0.85) x} x \cdot 7600

用

x ln (0.85) = u

和

x = \frac{u}{ln ( 0.85 )}

改写方程式

1500 = e^{u} (\frac{u}{ln ( 0.85 )}) \cdot 7600

改写

1500 = e^{u} (\frac{u}{ln ( 0.85 )}) 7600

为朗伯形式:

e^{u} u = \frac{15 ln ( 0.85 )}{76}

解

e^{u} u = \frac{15 ln ( 0.85 )}{76} : u = W_{- 1} (\frac{15 ln ( 0.85 )}{76}), u = W_{0} (\frac{15 ln ( 0.85 )}{76})

u = W_{- 1} (\frac{15 ln ( 0.85 )}{76}), u = W_{0} (\frac{15 ln ( 0.85 )}{76})

代回

u = x ln (0.85)

，求解

x

解

x ln (0.85) = W_{- 1} (\frac{15 ln ( 0.85 )}{76}) : x = \frac{W _{- 1} ( \frac{15 l n ( 0.85 )}{76} )}{ln ( 0.85 )}

解

x ln (0.85) = W_{0} (\frac{15 ln ( 0.85 )}{76}) : x = \frac{W _{0} ( \frac{15 l n ( 0.85 )}{76} )}{ln ( 0.85 )}

x = \frac{W _{- 1} ( \frac{15 l n ( 0.85 )}{76} )}{ln ( 0.85 )}, x = \frac{W _{0} ( \frac{15 l n ( 0.85 )}{76} )}{ln ( 0.85 )}

作图

流行的例子

4^{2x}-4^x=3*4^{x+1}

4^{2 x} - 4^{x} = 3 \cdot 4^{x + 1}

2 \cdot 5^{x} = 4^{x}

x = 1 - e^{- 2 x}

8 e^{\frac{x}{4}} = 1

solvefor y=e^{-x},x

so l v e f or y = e^{- x}, x