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人気のある代数 >

5^x+36x-97=0

解

5^{x} + 36 x - 97 = 0

解

x = - \frac{36 W _{0} ( \frac{e ^{\frac{97 l n ( 5 )}{36}} l n ( 5 )}{36} ) - 97 ln ( 5 )}{36 ln ( 5 )}

+1

十進法表記

x = 2

解答ステップ

5^{x} + 36 x - 97 = 0

ランベルト形式向けに

5^{x} + 36 x - 97 = 0

を準備する:

1 = - e^{- l n (5) x} (36 x - 97)

equationを

(- x + \frac{97}{36}) ln (5) = u

と以下で書き換える:

x = - \frac{36 u - 97 ln ( 5 )}{36 ln ( 5 )}

1 = - e^{- l n (5) (- \frac{36 u - 97 l n ( 5 )}{36 l n ( 5 )})} (36 (- \frac{36 u - 97 ln ( 5 )}{36 ln ( 5 )}) - 97)

簡素化

1 = - e^{\frac{36 u - 97 l n ( 5 )}{36}} (- \frac{36 u - 97 ln ( 5 )}{ln ( 5 )} - 97)

ランベルト形式で

1 = - e^{\frac{36 u - 97 l n ( 5 )}{36}} (- \frac{36 u - 97 ln ( 5 )}{ln ( 5 )} - 97)

を書き換える:

e^{u} u = \frac{e ^{\frac{97 l n ( 5 )}{36}} ln ( 5 )}{36}

解く

e^{u} u = \frac{e ^{\frac{97 l n ( 5 )}{36}} ln ( 5 )}{36} : u = W_{0} (\frac{e ^{\frac{97 l n ( 5 )}{36}} ln ( 5 )}{36})

u = W_{0} (\frac{e ^{\frac{97 l n ( 5 )}{36}} ln ( 5 )}{36})

再び

u = (- x + \frac{97}{36}) ln (5)

に置き換えて以下を解く:

x

解く

(- x + \frac{97}{36}) ln (5) = W_{0} (\frac{e ^{\frac{97 l n ( 5 )}{36}} ln ( 5 )}{36}) : x = - \frac{36 W _{0} ( \frac{e ^{\frac{97 l n ( 5 )}{36}} l n ( 5 )}{36} ) - 97 ln ( 5 )}{36 ln ( 5 )}

x = - \frac{36 W _{0} ( \frac{e ^{\frac{97 l n ( 5 )}{36}} l n ( 5 )}{36} ) - 97 ln ( 5 )}{36 ln ( 5 )}

グラフ

人気の例

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