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受欢迎的代数 >

solvefor a,(a^b)^2=b^a

解答

求解

a, (a^{b})^{2} = b^{a}

解答

a = - \frac{2 W ( - \frac{l n ( b )}{2 b} ) b}{ln ( b )}

求解步骤

(a^{b})^{2} = b^{a}

将

(a^{b})^{2} = b^{a}

调整为朗伯形式:

a e^{- \frac{a l n ( b )}{2 b}} = 1

用

- \frac{a ln ( b )}{2 b} = u

和

a = - \frac{2 b u}{ln ( b )}

改写方程式

(- \frac{2 b u}{ln ( b )}) e^{u} = 1

改写

(- \frac{2 b u}{ln ( b )}) e^{u} = 1

为朗伯形式:

e^{u} u = - \frac{ln ( b )}{2 b}

解

e^{u} u = - \frac{ln ( b )}{2 b} : u = W (- \frac{ln ( b )}{2 b})

u = W (- \frac{ln ( b )}{2 b})

代回

u = - \frac{a ln ( b )}{2 b}

，求解

a

解

- \frac{a ln ( b )}{2 b} = W (- \frac{ln ( b )}{2 b}) : a = - \frac{2 W ( - \frac{l n ( b )}{2 b} ) b}{ln ( b )}

a = - \frac{2 W ( - \frac{l n ( b )}{2 b} ) b}{ln ( b )}

作图

流行的例子

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

(15+5e^{4-x})/5+3=13

\frac{15 + 5 e ^{4 - x}}{5} + 3 = 13

4^{r} - 80 = 0

50e^{0.035x}=200

50 e^{0.035 x} = 200

3^{(x)} - 2 = 12