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人気のある代数 >

5(2x)=3(7^{4x-4})

解

5 (2 x) = 3 (7^{4 x - 4})

解

x = - \frac{W _{- 1} ( - \frac{6 l n ( 7 )}{12005} )}{4 ln ( 7 )}, x = - \frac{W _{0} ( - \frac{6 l n ( 7 )}{12005} )}{4 ln ( 7 )}

+1

十進法表記

x = 1.17544 \dots, x = 0.00012 \dots

解答ステップ

5 (2 x) = 3 (7^{4 x - 4})

ランベルト形式向けに

5 (2 x) = 3 (7^{4 x - 4})

を準備する:

10 e^{l n (7) (- 4 x + 4)} x = 3

equationを

- 4 x ln (7) = u

と以下で書き換える:

x = - \frac{u}{4 ln ( 7 )}

10 e^{l n (7) (- 4 (- \frac{u}{4 l n ( 7 )}) + 4)} (- \frac{u}{4 ln ( 7 )}) = 3

簡素化

- \frac{5 e ^{u + 4 l n (7)} u}{2 ln ( 7 )} = 3

ランベルト形式で

- \frac{5 e ^{u + 4 l n (7)} u}{2 ln ( 7 )} = 3

を書き換える:

e^{u} u = - \frac{6 ln ( 7 )}{12005}

解く

e^{u} u = - \frac{6 ln ( 7 )}{12005} : u = W_{- 1} (- \frac{6 ln ( 7 )}{12005}), u = W_{0} (- \frac{6 ln ( 7 )}{12005})

u = W_{- 1} (- \frac{6 ln ( 7 )}{12005}), u = W_{0} (- \frac{6 ln ( 7 )}{12005})

再び

u = - 4 x ln (7)

に置き換えて以下を解く:

x

解く

- 4 x ln (7) = W_{- 1} (- \frac{6 ln ( 7 )}{12005}) : x = - \frac{W _{- 1} ( - \frac{6 l n ( 7 )}{12005} )}{4 ln ( 7 )}

解く

- 4 x ln (7) = W_{0} (- \frac{6 ln ( 7 )}{12005}) : x = - \frac{W _{0} ( - \frac{6 l n ( 7 )}{12005} )}{4 ln ( 7 )}

x = - \frac{W _{- 1} ( - \frac{6 l n ( 7 )}{12005} )}{4 ln ( 7 )}, x = - \frac{W _{0} ( - \frac{6 l n ( 7 )}{12005} )}{4 ln ( 7 )}

グラフ

人気の例

2 e^{x} = 5

2^{x-1}5^{2x-3}=4

2^{x - 1} 5^{2 x - 3} = 4

2^{x+7}=2^{1-2x}

2^{x + 7} = 2^{1 - 2 x}

(4x)^{4x}=2^{24}

(4 x)^{4 x} = 2^{24}

solvefor x,g^{x+3}=81^{3x-7}

so l v e f or x, g^{x + 3} = 8 1^{3 x - 7}