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人気のある代数 >

2^{x-2}=8x

解

2^{x - 2} = 8 x

解

x = 8, x = - \frac{W _{0} ( - \frac{l n ( 2 )}{32} )}{ln ( 2 )}

+1

十進法表記

x = 8, x = 0.03194 \dots

解答ステップ

2^{x - 2} = 8 x

ランベルト形式向けに

2^{x - 2} = 8 x

を準備する:

1 = e^{l n (2) (- x + 5)} x

equationを

- x ln (2) = u

と以下で書き換える:

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

1 = e^{l n (2) (- (- \frac{u}{l n ( 2 )}) + 5)} (- \frac{u}{ln ( 2 )})

簡素化

1 = - \frac{e ^{u + 5 l n (2)} u}{ln ( 2 )}

ランベルト形式で

1 = - \frac{e ^{u + 5 l n (2)} u}{ln ( 2 )}

を書き換える:

e^{u} u = - \frac{ln ( 2 )}{32}

解く

e^{u} u = - \frac{ln ( 2 )}{32} : u = - 8 ln (2), u = W_{0} (- \frac{ln ( 2 )}{32})

u = - 8 ln (2), u = W_{0} (- \frac{ln ( 2 )}{32})

再び

u = - x ln (2)

に置き換えて以下を解く:

x

解く

- x ln (2) = - 8 ln (2) : x = 8

解く

- x ln (2) = W_{0} (- \frac{ln ( 2 )}{32}) : x = - \frac{W _{0} ( - \frac{l n ( 2 )}{32} )}{ln ( 2 )}

x = 8, x = - \frac{W _{0} ( - \frac{l n ( 2 )}{32} )}{ln ( 2 )}

グラフ

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