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人気のある代数 >

e^x=4x^{2+10}

解

e^{x} = 4 x^{2 + 10}

解

x = - 12 W_{- 1} (- \frac{1}{12 e ^{\frac{l n ( 2 )}{6}}}), x = - 12 W_{0} (- \frac{1}{12 e ^{\frac{l n ( 2 )}{6}}})

+1

十進法表記

x = 47.78745 \dots, x = 0.96554 \dots

解答ステップ

e^{x} = 4 x^{2 + 10}

ランベルト形式向けに

e^{x} = 4 x^{2 + 10}

を準備する:

1 = 62 x e^{- \frac{x}{12}}

equationを

- \frac{x}{12} = u

と以下で書き換える:

x = - 12 u

1 = 62 (- 12 u) e^{u}

ランベルト形式で

1 = 62 (- 12 u) e^{u}

を書き換える:

\frac{2 ^{\frac{6 l o g _{2} ( e ) u + 1}{6}} u}{e ^{\frac{l n ( 2 )}{6}}} = - \frac{1}{12 e ^{\frac{l n ( 2 )}{6}}}

解く

\frac{2 ^{\frac{6 l o g _{2} ( e ) u + 1}{6}} u}{e ^{\frac{l n ( 2 )}{6}}} = - \frac{1}{12 e ^{\frac{l n ( 2 )}{6}}} : u = W_{- 1} (- \frac{1}{12 e ^{\frac{l n ( 2 )}{6}}}), u = W_{0} (- \frac{1}{12 e ^{\frac{l n ( 2 )}{6}}})

u = W_{- 1} (- \frac{1}{12 e ^{\frac{l n ( 2 )}{6}}}), u = W_{0} (- \frac{1}{12 e ^{\frac{l n ( 2 )}{6}}})

再び

u = - \frac{x}{12}

に置き換えて以下を解く:

x

解く

- \frac{x}{12} = W_{- 1} (- \frac{1}{12 e ^{\frac{l n ( 2 )}{6}}}) : x = - 12 W_{- 1} (- \frac{1}{12 e ^{\frac{l n ( 2 )}{6}}})

解く

- \frac{x}{12} = W_{0} (- \frac{1}{12 e ^{\frac{l n ( 2 )}{6}}}) : x = - 12 W_{0} (- \frac{1}{12 e ^{\frac{l n ( 2 )}{6}}})

x = - 12 W_{- 1} (- \frac{1}{12 e ^{\frac{l n ( 2 )}{6}}}), x = - 12 W_{0} (- \frac{1}{12 e ^{\frac{l n ( 2 )}{6}}})

グラフ

人気の例

10 = 5 e^{5 x}

2^{2x}-5(2^x)+4=0

2^{2 x} - 5 (2^{x}) + 4 = 0

e^{-3}e^2ln(e^e)=e^x

e^{- 3} e^{2} ln (e^{e}) = e^{x}

5^{x^{2}} = 17

3^t=\sqrt[5]{3}

3^{t} = 53