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人気のある代数 >

4x-5.2^x+4=0

解

4 x - 5. 2^{x} + 4 = 0

解

x = - \frac{W _{- 1} ( - \frac{l n ( 5.2 )}{20.8} ) + ln ( 5.2 )}{ln ( 5.2 )}, x = - \frac{W _{0} ( - \frac{l n ( 5.2 )}{20.8} ) + ln ( 5.2 )}{ln ( 5.2 )}

+1

十進法表記

x = 1.36226 \dots, x = - 0.94758 \dots

解答ステップ

4 x - 5. 2^{x} + 4 = 0

ランベルト形式向けに

4 x - 5. 2^{x} + 4 = 0

を準備する:

- 1 = - e^{- l n (5.2) x} (4 x + 4)

equationを

(- x - 1) ln (5.2) = u

と以下で書き換える:

x = - \frac{u + ln ( 5.2 )}{ln ( 5.2 )}

- 1 = - e^{- l n (5.2) (- \frac{u + l n ( 5.2 )}{l n ( 5.2 )})} (4 (- \frac{u + ln ( 5.2 )}{ln ( 5.2 )}) + 4)

簡素化

- 1 = - e^{u + l n (5.2)} (- \frac{4 ( u + ln ( 5.2 ) )}{ln ( 5.2 )} + 4)

ランベルト形式で

- 1 = - e^{u + l n (5.2)} (- \frac{4 ( u + ln ( 5.2 ) )}{ln ( 5.2 )} + 4)

を書き換える:

e^{u} u = - \frac{ln ( 5.2 )}{20.8}

解く

e^{u} u = - \frac{ln ( 5.2 )}{20.8} : u = W_{- 1} (- \frac{ln ( 5.2 )}{20.8}), u = W_{0} (- \frac{ln ( 5.2 )}{20.8})

u = W_{- 1} (- \frac{ln ( 5.2 )}{20.8}), u = W_{0} (- \frac{ln ( 5.2 )}{20.8})

再び

u = (- x - 1) ln (5.2)

に置き換えて以下を解く:

x

解く

(- x - 1) ln (5.2) = W_{- 1} (- \frac{ln ( 5.2 )}{20.8}) : x = - \frac{W _{- 1} ( - \frac{l n ( 5.2 )}{20.8} ) + ln ( 5.2 )}{ln ( 5.2 )}

解く

(- x - 1) ln (5.2) = W_{0} (- \frac{ln ( 5.2 )}{20.8}) : x = - \frac{W _{0} ( - \frac{l n ( 5.2 )}{20.8} ) + ln ( 5.2 )}{ln ( 5.2 )}

x = - \frac{W _{- 1} ( - \frac{l n ( 5.2 )}{20.8} ) + ln ( 5.2 )}{ln ( 5.2 )}, x = - \frac{W _{0} ( - \frac{l n ( 5.2 )}{20.8} ) + ln ( 5.2 )}{ln ( 5.2 )}

グラフ

人気の例

3^{15}k= 1/(27^k)+3

3^{15} k = \frac{1}{2 7 ^{k}} + 3

(b)5^{2x+1}=125

(b) 5^{2 x + 1} = 125

7^{x} - 7^{- x} = 7

3^{x} = \frac{1}{27}

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

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