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人気のある代数 >

2^{x-1}=3x

解

2^{x - 1} = 3 x

解

x = - \frac{W _{- 1} ( - \frac{l n ( 2 )}{6} )}{ln ( 2 )}, x = - \frac{W _{0} ( - \frac{l n ( 2 )}{6} )}{ln ( 2 )}

+1

十進法表記

x = 4.86841 \dots, x = 0.19014 \dots

解答ステップ

2^{x - 1} = 3 x

ランベルト形式向けに

2^{x - 1} = 3 x

を準備する:

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

equationを

- x ln (2) = u

と以下で書き換える:

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

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

簡素化

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

ランベルト形式で

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

を書き換える:

e^{u} u = - \frac{ln ( 2 )}{6}

解く

e^{u} u = - \frac{ln ( 2 )}{6} : u = W_{- 1} (- \frac{ln ( 2 )}{6}), u = W_{0} (- \frac{ln ( 2 )}{6})

u = W_{- 1} (- \frac{ln ( 2 )}{6}), u = W_{0} (- \frac{ln ( 2 )}{6})

再び

u = - x ln (2)

に置き換えて以下を解く:

x

解く

- x ln (2) = W_{- 1} (- \frac{ln ( 2 )}{6}) : x = - \frac{W _{- 1} ( - \frac{l n ( 2 )}{6} )}{ln ( 2 )}

解く

- x ln (2) = W_{0} (- \frac{ln ( 2 )}{6}) : x = - \frac{W _{0} ( - \frac{l n ( 2 )}{6} )}{ln ( 2 )}

x = - \frac{W _{- 1} ( - \frac{l n ( 2 )}{6} )}{ln ( 2 )}, x = - \frac{W _{0} ( - \frac{l n ( 2 )}{6} )}{ln ( 2 )}

グラフ

人気の例

2^{- x} = 0

e^{8 - 4 x} = 9

e^{8 - 4 x} = 4

1 0^{x} = \frac{1}{100}

5^{x - 2} = 625