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人気のある代数 >

2^x=x+2

解

2^{x} = x + 2

解

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

+1

十進法表記

x = 2, x = - 1.69009 \dots

解答ステップ

2^{x} = x + 2

ランベルト形式向けに

2^{x} = x + 2

を準備する:

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

equationを

(- x - 2) ln (2) = u

と以下で書き換える:

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

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

簡素化

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

ランベルト形式で

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

を書き換える:

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

解く

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

に置き換えて以下を解く:

x

解く

(- x - 2) ln (2) = - 4 ln (2) : x = 2

解く

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

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

グラフ

人気の例

15 \cdot 5^{x} = 53 \cdot 2^{x}

5^{x} = 120

2^{x+7}*4^{x-1}=8^{2x+3}

2^{x + 7} \cdot 4^{x - 1} = 8^{2 x + 3}

6^{2 x - 7} = 216

3^{x^2-4x+1}= 1/81

3^{x^{2} - 4 x + 1} = \frac{1}{81}