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受欢迎的代数 >

a^a=2

解答

a^{a} = 2

解答

a = \frac{ln ( 2 )}{W _{0} ( ln ( 2 ) )}

+1

十进制

a = 1.55961 \dots

求解步骤

a^{a} = 2

将

a^{a} = 2

调整为朗伯形式:

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

用

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

和

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

改写方程式

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

改写

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

为朗伯形式:

u e^{u} = ln (2)

解

u e^{u} = ln (2) : u = W_{0} (ln (2))

验证解:

u = W_{0} (ln (2))

真

解是

u = W_{0} (ln (2))

代回

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

，求解

a

解

\frac{ln ( 2 )}{a} = W_{0} (ln (2)) : a = \frac{ln ( 2 )}{W _{0} ( ln ( 2 ) )}

a = \frac{ln ( 2 )}{W _{0} ( ln ( 2 ) )}

作图

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