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人気のある代数 >

55=5+ce^{((ln(50))/c)}

解

55 = 5 + c e^{(\frac{l n ( 50 )}{c})}

解

c = 1, c = - \frac{ln ( 50 )}{W _{0} ( - \frac{l n ( 50 )}{50} )}

+1

十進法表記

c = 1, c = 45.91649 \dots

解答ステップ

55 = 5 + c e^{(\frac{l n ( 50 )}{c})}

ランベルト形式向けに

55 = 5 + c e^{(\frac{l n ( 50 )}{c})}

を準備する:

c e^{\frac{l n ( 50 )}{c}} = 50

equationを

- \frac{ln ( 50 )}{c} = u

と以下で書き換える:

c = - \frac{ln ( 50 )}{u}

(- \frac{ln ( 50 )}{u}) e^{- u} = 50

ランベルト形式で

(- \frac{ln ( 50 )}{u}) e^{- u} = 50

を書き換える:

e^{u} u = - \frac{ln ( 50 )}{50}

解く

e^{u} u = - \frac{ln ( 50 )}{50} : u = - ln (50), u = W_{0} (- \frac{ln ( 50 )}{50})

u = - ln (50), u = W_{0} (- \frac{ln ( 50 )}{50})

再び

u = - \frac{ln ( 50 )}{c}

に置き換えて以下を解く:

c

解く

- \frac{ln ( 50 )}{c} = - ln (50) : c = 1

解く

- \frac{ln ( 50 )}{c} = W_{0} (- \frac{ln ( 50 )}{50}) : c = - \frac{ln ( 50 )}{W _{0} ( - \frac{l n ( 50 )}{50} )}

c = 1, c = - \frac{ln ( 50 )}{W _{0} ( - \frac{l n ( 50 )}{50} )}

グラフ

人気の例

25^{x+2}=125^{x+1}

2 5^{x + 2} = 12 5^{x + 1}

solvefor x,3^{2x}+3^{-2x}=14

so l v e f or x, 3^{2 x} + 3^{- 2 x} = 14

7^{2 - x} = 343

3^{3 x - 2} = \frac{1}{54}

45 e^{2 k} = 225