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人気のある代数 >

n=2^{n/8}

解

n = 2^{\frac{n}{8}}

解

n = - \frac{8 W _{- 1} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}, n = - \frac{8 W _{0} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}

+1

十進法表記

n = 43.55926 \dots, n = 1.09999 \dots

解答ステップ

n = 2^{\frac{n}{8}}

ランベルト形式向けに

n = 2^{\frac{n}{8}}

を準備する:

n e^{- \frac{l n ( 2 ) n}{8}} = 1

equationを

- \frac{ln ( 2 ) n}{8} = u

と以下で書き換える:

n = - \frac{8 u}{ln ( 2 )}

(- \frac{8 u}{ln ( 2 )}) e^{u} = 1

ランベルト形式で

(- \frac{8 u}{ln ( 2 )}) e^{u} = 1

を書き換える:

e^{u} u = - \frac{ln ( 2 )}{8}

解く

e^{u} u = - \frac{ln ( 2 )}{8} : u = W_{- 1} (- \frac{ln ( 2 )}{8}), u = W_{0} (- \frac{ln ( 2 )}{8})

u = W_{- 1} (- \frac{ln ( 2 )}{8}), u = W_{0} (- \frac{ln ( 2 )}{8})

再び

u = - \frac{ln ( 2 ) n}{8}

に置き換えて以下を解く:

n

解く

- \frac{ln ( 2 ) n}{8} = W_{- 1} (- \frac{ln ( 2 )}{8}) : n = - \frac{8 W _{- 1} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}

解く

- \frac{ln ( 2 ) n}{8} = W_{0} (- \frac{ln ( 2 )}{8}) : n = - \frac{8 W _{0} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}

n = - \frac{8 W _{- 1} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}, n = - \frac{8 W _{0} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}

グラフ

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