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人気のある代数 >

0.9711n-0.9711=(0.9614)^n

解

0.9711 n - 0.9711 = (0.9614)^{n}

解

n = - \frac{W _{0} ( - \frac{0.92428996 l n ( 0.9614 )}{0.93361554} ) - ln ( 0.9614 )}{ln ( 0.9614 )}

+1

十進法表記

n = 1.95353 \dots

解答ステップ

0.9711 n - 0.9711 = (0.9614)^{n}

ランベルト形式向けに

0.9711 n - 0.9711 = (0.9614)^{n}

を準備する:

1 = 0.9711 (n - 1) e^{- l n (0.9614) n}

equationを

(- n + 1) ln (0.9614) = u

と以下で書き換える:

n = - \frac{u - ln ( 0.9614 )}{ln ( 0.9614 )}

1 = 0.9711 ((- \frac{u - ln ( 0.9614 )}{ln ( 0.9614 )}) - 1) e^{- l n (0.9614) (- \frac{u - l n ( 0.9614 )}{l n ( 0.9614 )})}

簡素化

1 = 0.9711 e^{u - l n (0.9614)} (- \frac{u - ln ( 0.9614 )}{ln ( 0.9614 )} - 1)

ランベルト形式で

1 = 0.9711 e^{u - l n (0.9614)} (- \frac{u - ln ( 0.9614 )}{ln ( 0.9614 )} - 1)

を書き換える:

e^{u} u = - \frac{0.92428996 ln ( 0.9614 )}{0.93361554}

解く

e^{u} u = - \frac{0.92428996 ln ( 0.9614 )}{0.93361554} : u = W_{0} (- \frac{0.92428996 ln ( 0.9614 )}{0.93361554})

u = W_{0} (- \frac{0.92428996 ln ( 0.9614 )}{0.93361554})

再び

u = (- n + 1) ln (0.9614)

に置き換えて以下を解く:

n

解く

(- n + 1) ln (0.9614) = W_{0} (- \frac{0.92428996 ln ( 0.9614 )}{0.93361554}) : n = - \frac{W _{0} ( - \frac{0.92428996 l n ( 0.9614 )}{0.93361554} ) - ln ( 0.9614 )}{ln ( 0.9614 )}

n = - \frac{W _{0} ( - \frac{0.92428996 l n ( 0.9614 )}{0.93361554} ) - ln ( 0.9614 )}{ln ( 0.9614 )}

グラフ

人気の例

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