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人気のある代数 >

6x= 10/3-6^{-x}

解

6 x = \frac{10}{3} - 6^{- x}

解

x = \frac{W _{- 1} ( - \frac{l n ( 6 )}{6 e ^{\frac{5 l n ( 6 )}{9}}} )}{ln ( 6 )} + \frac{5}{9}, x = \frac{W _{0} ( - \frac{l n ( 6 )}{6 e ^{\frac{5 l n ( 6 )}{9}}} )}{ln ( 6 )} + \frac{5}{9}

+1

十進法表記

x = - 1.36391 \dots, x = 0.48575 \dots

解答ステップ

6 x = \frac{10}{3} - 6^{- x}

ランベルト形式向けに

6 x = \frac{10}{3} - 6^{- x}

を準備する:

- 1 = (6 x - \frac{10}{3}) e^{l n (6) x}

equationを

(x - \frac{5}{9}) ln (6) = u

と以下で書き換える:

x = \frac{u}{ln ( 6 )} + \frac{5}{9}

- 1 = (6 (\frac{u}{ln ( 6 )} + \frac{5}{9}) - \frac{10}{3}) e^{l n (6) (\frac{u}{l n ( 6 )} + \frac{5}{9})}

簡素化

- 1 = \frac{6 e ^{u + \frac{5}{9} l n (6)} u}{ln ( 6 )}

ランベルト形式で

- 1 = \frac{6 e ^{u + \frac{5}{9} l n (6)} u}{ln ( 6 )}

を書き換える:

\frac{e ^{\frac{9 u + 5 l n ( 6 )}{9}} u}{e ^{\frac{5 l n ( 6 )}{9}}} = - \frac{ln ( 6 )}{6 e ^{\frac{5 l n ( 6 )}{9}}}

解く

\frac{e ^{\frac{9 u + 5 l n ( 6 )}{9}} u}{e ^{\frac{5 l n ( 6 )}{9}}} = - \frac{ln ( 6 )}{6 e ^{\frac{5 l n ( 6 )}{9}}} : u = W_{- 1} (- \frac{ln ( 6 )}{6 e ^{\frac{5 l n ( 6 )}{9}}}), u = W_{0} (- \frac{ln ( 6 )}{6 e ^{\frac{5 l n ( 6 )}{9}}})

u = W_{- 1} (- \frac{ln ( 6 )}{6 e ^{\frac{5 l n ( 6 )}{9}}}), u = W_{0} (- \frac{ln ( 6 )}{6 e ^{\frac{5 l n ( 6 )}{9}}})

再び

u = (x - \frac{5}{9}) ln (6)

に置き換えて以下を解く:

x

解く

(x - \frac{5}{9}) ln (6) = W_{- 1} (- \frac{ln ( 6 )}{6 e ^{\frac{5 l n ( 6 )}{9}}}) : x = \frac{W _{- 1} ( - \frac{l n ( 6 )}{6 e ^{\frac{5 l n ( 6 )}{9}}} )}{ln ( 6 )} + \frac{5}{9}

解く

(x - \frac{5}{9}) ln (6) = W_{0} (- \frac{ln ( 6 )}{6 e ^{\frac{5 l n ( 6 )}{9}}}) : x = \frac{W _{0} ( - \frac{l n ( 6 )}{6 e ^{\frac{5 l n ( 6 )}{9}}} )}{ln ( 6 )} + \frac{5}{9}

x = \frac{W _{- 1} ( - \frac{l n ( 6 )}{6 e ^{\frac{5 l n ( 6 )}{9}}} )}{ln ( 6 )} + \frac{5}{9}, x = \frac{W _{0} ( - \frac{l n ( 6 )}{6 e ^{\frac{5 l n ( 6 )}{9}}} )}{ln ( 6 )} + \frac{5}{9}

グラフ

人気の例

2^{x - 3} = 16

2^{8^{x-2}}=4^{4^{x+1}}

2^{8^{x - 2}} = 4^{4^{x + 1}}

e^{3x}=(e^2)/(e^x)

e^{3 x} = \frac{e ^{2}}{e ^{x}}

3^{y} = 6

7^{x} = 3^{x + 4}