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受欢迎的代数 >

a^x=5+x

解答

a^{x} = 5 + x

解答

x = - \frac{W ( - \frac{l n ( a )}{a ^{5}} ) + 5 ln ( a )}{ln ( a )}

求解步骤

a^{x} = 5 + x

将

a^{x} = 5 + x

调整为朗伯形式:

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

用

(- x - 5) ln (a) = u

和

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

改写方程式

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

化简

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

改写

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

为朗伯形式:

e^{u} u = - \frac{ln ( a )}{a ^{5}}

解

e^{u} u = - \frac{ln ( a )}{a ^{5}} : u = W (- \frac{ln ( a )}{a ^{5}})

u = W (- \frac{ln ( a )}{a ^{5}})

代回

u = (- x - 5) ln (a)

，求解

x

解

(- x - 5) ln (a) = W (- \frac{ln ( a )}{a ^{5}}) : x = - \frac{W ( - \frac{l n ( a )}{a ^{5}} ) + 5 ln ( a )}{ln ( a )}

x = - \frac{W ( - \frac{l n ( a )}{a ^{5}} ) + 5 ln ( a )}{ln ( a )}

作图

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