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人気のある代数 >

x^{sqrt(x)}=10

解

x^{x} = 10

解

x = \frac{ln ^{2} ( 10 )}{4 W _{0} ( \frac{l n ( 10 )}{2} ) ^{2}}

+1

十進法表記

x = 3.45276 \dots

解答ステップ

x^{x} = 10

ランベルト形式向けに

x^{x} = 10

を準備する:

x e^{- \frac{l n ( 10 )}{x}} = 1

equationを

\frac{ln ( 10 )}{x} = u

と以下で書き換える:

x = \frac{ln ^{2} ( 10 )}{u ^{2}}

(\frac{ln ^{2} ( 10 )}{u ^{2}}) e^{- u} = 1

解く

(\frac{ln ^{2} ( 10 )}{u ^{2}}) e^{- u} = 1 : u = 2 W_{0} (\frac{ln ( 10 )}{2})

u = 2 W_{0} (\frac{ln ( 10 )}{2})

再び

u = \frac{ln ( 10 )}{x}

に置き換えて以下を解く:

x

解く

\frac{ln ( 10 )}{x} = 2 W_{0} (\frac{ln ( 10 )}{2}) : x = \frac{ln ^{2} ( 10 )}{4 W _{0} ( \frac{l n ( 10 )}{2} ) ^{2}}

x = \frac{ln ^{2} ( 10 )}{4 W _{0} ( \frac{l n ( 10 )}{2} ) ^{2}}

解を検算する:

x = \frac{ln ^{2} ( 10 )}{4 W _{0} ( \frac{l n ( 10 )}{2} ) ^{2}}

真

解は

x = \frac{ln ^{2} ( 10 )}{4 W _{0} ( \frac{l n ( 10 )}{2} ) ^{2}}

解を検算する:

x = \frac{ln ^{2} ( 10 )}{4 W _{0} ( \frac{l n ( 10 )}{2} ) ^{2}}

真

解は

x = \frac{ln ^{2} ( 10 )}{4 W _{0} ( \frac{l n ( 10 )}{2} ) ^{2}}

グラフ

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