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人気のある代数 >

solvefor x,3^{2x}+1+4(3x)-15=0

解

解く

x, 3^{2 x} + 1 + 4 (3 x) - 15 = 0

解

x = - \frac{3 W _{0} ( \frac{e ^{\frac{7 l n ( 3 )}{3}} l n ( 3 )}{6} ) - 7 ln ( 3 )}{6 ln ( 3 )}

+1

十進法表記

x = 0.74158 \dots

解答ステップ

3^{2 x} + 1 + 4 (3 x) - 15 = 0

ランベルト形式向けに

3^{2 x} + 1 + 4 (3 x) - 15 = 0

を準備する:

1 = - e^{- 2 l n (3) x} (12 x - 14)

equationを

2 ln (3) (- x + \frac{7}{6}) = u

と以下で書き換える:

x = - \frac{3 u - 7 ln ( 3 )}{6 ln ( 3 )}

1 = - e^{- 2 l n (3) (- \frac{3 u - 7 l n ( 3 )}{6 l n ( 3 )})} (12 (- \frac{3 u - 7 ln ( 3 )}{6 ln ( 3 )}) - 14)

簡素化

1 = - e^{\frac{3 u - 7 l n ( 3 )}{3}} (- \frac{2 ( 3 u - 7 ln ( 3 ) )}{ln ( 3 )} - 14)

ランベルト形式で

1 = - e^{\frac{3 u - 7 l n ( 3 )}{3}} (- \frac{2 ( 3 u - 7 ln ( 3 ) )}{ln ( 3 )} - 14)

を書き換える:

e^{u} u = \frac{e ^{\frac{7 l n ( 3 )}{3}} ln ( 3 )}{6}

解く

e^{u} u = \frac{e ^{\frac{7 l n ( 3 )}{3}} ln ( 3 )}{6} : u = W_{0} (\frac{e ^{\frac{7 l n ( 3 )}{3}} ln ( 3 )}{6})

u = W_{0} (\frac{e ^{\frac{7 l n ( 3 )}{3}} ln ( 3 )}{6})

再び

u = 2 ln (3) (- x + \frac{7}{6})

に置き換えて以下を解く:

x

解く

2 ln (3) (- x + \frac{7}{6}) = W_{0} (\frac{e ^{\frac{7 l n ( 3 )}{3}} ln ( 3 )}{6}) : x = - \frac{3 W _{0} ( \frac{e ^{\frac{7 l n ( 3 )}{3}} l n ( 3 )}{6} ) - 7 ln ( 3 )}{6 ln ( 3 )}

x = - \frac{3 W _{0} ( \frac{e ^{\frac{7 l n ( 3 )}{3}} l n ( 3 )}{6} ) - 7 ln ( 3 )}{6 ln ( 3 )}

グラフ

人気の例

xe^{2x}=xe^{x+3}

x e^{2 x} = x e^{x + 3}

2 = 1. 1^{t}

15=45e^{-0.05t}

15 = 45 e^{- 0.05 t}

3^{4x-2}=9^{-(x+1)}

3^{4 x - 2} = 9^{- (x + 1)}

2xe^{x^2}=x^2e^{x^2}

2 x e^{x^{2}} = x^{2} e^{x^{2}}