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人気のある代数 >

2^x+4x+12=0

解

2^{x} + 4 x + 12 = 0

解

x = - \frac{W _{0} ( \frac{l n ( 2 )}{32} ) + 3 ln ( 2 )}{ln ( 2 )}

+1

十進法表記

x = - 3.03059 \dots

解答ステップ

2^{x} + 4 x + 12 = 0

ランベルト形式向けに

2^{x} + 4 x + 12 = 0

を準備する:

1 = - e^{- l n (2) x} (4 x + 12)

equationを

(- x - 3) ln (2) = u

と以下で書き換える:

x = - \frac{u + 3 ln ( 2 )}{ln ( 2 )}

1 = - e^{- l n (2) (- \frac{u + 3 l n ( 2 )}{l n ( 2 )})} (4 (- \frac{u + 3 ln ( 2 )}{ln ( 2 )}) + 12)

簡素化

1 = - e^{u + 3 l n (2)} (- \frac{4 ( u + 3 ln ( 2 ) )}{ln ( 2 )} + 12)

ランベルト形式で

1 = - e^{u + 3 l n (2)} (- \frac{4 ( u + 3 ln ( 2 ) )}{ln ( 2 )} + 12)

を書き換える:

e^{u} u = \frac{ln ( 2 )}{32}

解く

e^{u} u = \frac{ln ( 2 )}{32} : u = W_{0} (\frac{ln ( 2 )}{32})

u = W_{0} (\frac{ln ( 2 )}{32})

再び

u = (- x - 3) ln (2)

に置き換えて以下を解く:

x

解く

(- x - 3) ln (2) = W_{0} (\frac{ln ( 2 )}{32}) : x = - \frac{W _{0} ( \frac{l n ( 2 )}{32} ) + 3 ln ( 2 )}{ln ( 2 )}

x = - \frac{W _{0} ( \frac{l n ( 2 )}{32} ) + 3 ln ( 2 )}{ln ( 2 )}

グラフ

人気の例

5e^{2-x}=10^{x+4}

5 e^{2 - x} = 1 0^{x + 4}

-(16x-16)e^{-x}=0

- (16 x - 16) e^{- x} = 0

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2^{x + 1} + 6 (2^{x - 1}) = 12

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