ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある代数 >

x^x=sqrt((\sqrt{2))/2}

解

x^{x} = \frac{2}{2}

解

x = \frac{1}{16}, x = - \frac{ln ( 2 )}{4 W _{0} ( - \frac{l n ( 2 )}{4} )}

+1

十進法表記

x = 0.0625, x = 0.80669 \dots

解答ステップ

x^{x} = \frac{2}{2}

ランベルト形式向けに

x^{x} = \frac{2}{2}

を準備する:

x e^{\frac{l n ( 2 )}{4 x}} = 1

equationを

- \frac{ln ( 2 )}{4 x} = u

と以下で書き換える:

x = - \frac{ln ( 2 )}{4 u}

(- \frac{ln ( 2 )}{4 u}) e^{- u} = 1

解く

(- \frac{ln ( 2 )}{4 u}) e^{- u} = 1 : u = - 4 ln (2), u = W_{0} (- \frac{ln ( 2 )}{4})

u = - 4 ln (2), u = W_{0} (- \frac{ln ( 2 )}{4})

再び

u = - \frac{ln ( 2 )}{4 x}

に置き換えて以下を解く:

x

解く

- \frac{ln ( 2 )}{4 x} = - 4 ln (2) : x = \frac{1}{16}

解く

- \frac{ln ( 2 )}{4 x} = W_{0} (- \frac{ln ( 2 )}{4}) : x = - \frac{ln ( 2 )}{4 W _{0} ( - \frac{l n ( 2 )}{4} )}

x = \frac{1}{16}, x = - \frac{ln ( 2 )}{4 W _{0} ( - \frac{l n ( 2 )}{4} )}

グラフ

人気の例

256^{3x+3}=1024^{2x+2}

25 6^{3 x + 3} = 102 4^{2 x + 2}

216 = 6^{2 r - 11}

2^{x-x^2}= 1/(4^x)

2^{x - x^{2}} = \frac{1}{4 ^{x}}

625^x= 1/(sqrt(5))

62 5^{x} = \frac{1}{5}

2 5^{v - 2} = 625