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受欢迎的代数 >

5^{(-x)}+7=2x+4

解答

5^{(- x)} + 7 = 2 x + 4

解答

x = \frac{W _{0} ( \frac{l n ( 5 )}{2 e ^{\frac{3 l n ( 5 )}{2}}} )}{ln ( 5 )} + \frac{3}{2}

+1

十进制

x = 1.54181 \dots

求解步骤

5^{(- x)} + 7 = 2 x + 4

将

5^{(- x)} + 7 = 2 x + 4

调整为朗伯形式:

1 = (2 x - 3) e^{l n (5) x}

用

(x - \frac{3}{2}) ln (5) = u

和

x = \frac{u}{ln ( 5 )} + \frac{3}{2}

改写方程式

1 = (2 (\frac{u}{ln ( 5 )} + \frac{3}{2}) - 3) e^{l n (5) (\frac{u}{l n ( 5 )} + \frac{3}{2})}

化简

1 = \frac{2 e ^{u + \frac{3}{2} l n (5)} u}{ln ( 5 )}

改写

1 = \frac{2 e ^{u + \frac{3}{2} l n (5)} u}{ln ( 5 )}

为朗伯形式:

\frac{e ^{\frac{2 u + 3 l n ( 5 )}{2}} u}{e ^{\frac{3 l n ( 5 )}{2}}} = \frac{ln ( 5 )}{2 e ^{\frac{3 l n ( 5 )}{2}}}

解

\frac{e ^{\frac{2 u + 3 l n ( 5 )}{2}} u}{e ^{\frac{3 l n ( 5 )}{2}}} = \frac{ln ( 5 )}{2 e ^{\frac{3 l n ( 5 )}{2}}} : u = W_{0} (\frac{ln ( 5 )}{2 e ^{\frac{3 l n ( 5 )}{2}}})

u = W_{0} (\frac{ln ( 5 )}{2 e ^{\frac{3 l n ( 5 )}{2}}})

代回

u = (x - \frac{3}{2}) ln (5)

，求解

x

解

(x - \frac{3}{2}) ln (5) = W_{0} (\frac{ln ( 5 )}{2 e ^{\frac{3 l n ( 5 )}{2}}}) : x = \frac{W _{0} ( \frac{l n ( 5 )}{2 e ^{\frac{3 l n ( 5 )}{2}}} )}{ln ( 5 )} + \frac{3}{2}

x = \frac{W _{0} ( \frac{l n ( 5 )}{2 e ^{\frac{3 l n ( 5 )}{2}}} )}{ln ( 5 )} + \frac{3}{2}

作图

流行的例子

8^{- 5 a} - 5 = 53

m=-3(5)^{n+4}-1/2

m = - 3 (5)^{n + 4} - \frac{1}{2}

3^{x} = 45

3^{x} = - 6

2^{p} = \frac{1}{8 ^{4}}