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人気のある代数 >

x^{sqrt(x)}=2

解

x^{x} = 2

解

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

+1

十進法表記

x = 1.70133 \dots

解答ステップ

x^{x} = 2

ランベルト形式向けに

x^{x} = 2

を準備する:

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

equationを

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

と以下で書き換える:

x = \frac{ln ^{2} ( 2 )}{u ^{2}}

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

解く

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

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

再び

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

に置き換えて以下を解く:

x

解く

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

以下の解はない:

x \in R

解く

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

以下の解はない:

x \in R

解く

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

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

解を検算する:

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

真

解は

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

解を検算する:

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

真

解は

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

グラフ

人気の例

4^{3x-1}=(0.5)^{-x-3}

4^{3 x - 1} = (0.5)^{- x - 3}

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e^{- x^{2} - y^{2}} x (1 - 2 y^{2}) = 0

\frac{n}{2 ^{x}} = 1

550 \cdot 3^{x} = 50

(8^x+1)/(8^x)=9

\frac{8 ^{x} + 1}{8 ^{x}} = 9