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人気のある代数 >

2=2^t-2t

解

2 = 2^{t} - 2 t

解

t = 3, t = - \frac{W _{0} ( - \frac{l n ( 2 )}{4} ) + ln ( 2 )}{ln ( 2 )}

+1

十進法表記

t = 3, t = - 0.69009 \dots

解答ステップ

2 = 2^{t} - 2 t

ランベルト形式向けに

2 = 2^{t} - 2 t

を準備する:

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

equationを

(- t - 1) ln (2) = u

と以下で書き換える:

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

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

簡素化

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

ランベルト形式で

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

に置き換えて以下を解く:

t

解く

(- t - 1) ln (2) = - 4 ln (2) : t = 3

解く

(- t - 1) ln (2) = W_{0} (- \frac{ln ( 2 )}{4}) : t = - \frac{W _{0} ( - \frac{l n ( 2 )}{4} ) + ln ( 2 )}{ln ( 2 )}

t = 3, t = - \frac{W _{0} ( - \frac{l n ( 2 )}{4} ) + ln ( 2 )}{ln ( 2 )}

グラフ

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