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人気のある代数 >

2^2x-6.2^x+8=0

解

2^{2} x - 6. 2^{x} + 8 = 0

解

x = - \frac{W _{- 1} ( - \frac{l n ( 6.2 )}{153.76} ) + 2 ln ( 6.2 )}{ln ( 6.2 )}, x = - \frac{W _{0} ( - \frac{l n ( 6.2 )}{153.76} ) + 2 ln ( 6.2 )}{ln ( 6.2 )}

+1

十進法表記

x = 1.43635 \dots, x = - 1.99341 \dots

解答ステップ

2^{2} x - 6. 2^{x} + 8 = 0

ランベルト形式向けに

2^{2} x - 6. 2^{x} + 8 = 0

を準備する:

- 1 = - e^{- l n (6.2) x} (4 x + 8)

equationを

(- x - 2) ln (6.2) = u

と以下で書き換える:

x = - \frac{u + 2 ln ( 6.2 )}{ln ( 6.2 )}

- 1 = - e^{- l n (6.2) (- \frac{u + 2 l n ( 6.2 )}{l n ( 6.2 )})} (4 (- \frac{u + 2 ln ( 6.2 )}{ln ( 6.2 )}) + 8)

簡素化

- 1 = - e^{u + 2 l n (6.2)} (- \frac{4 ( u + 2 ln ( 6.2 ) )}{ln ( 6.2 )} + 8)

ランベルト形式で

- 1 = - e^{u + 2 l n (6.2)} (- \frac{4 ( u + 2 ln ( 6.2 ) )}{ln ( 6.2 )} + 8)

を書き換える:

e^{u} u = - \frac{ln ( 6.2 )}{153.76}

解く

e^{u} u = - \frac{ln ( 6.2 )}{153.76} : u = W_{- 1} (- \frac{ln ( 6.2 )}{153.76}), u = W_{0} (- \frac{ln ( 6.2 )}{153.76})

u = W_{- 1} (- \frac{ln ( 6.2 )}{153.76}), u = W_{0} (- \frac{ln ( 6.2 )}{153.76})

再び

u = (- x - 2) ln (6.2)

に置き換えて以下を解く:

x

解く

(- x - 2) ln (6.2) = W_{- 1} (- \frac{ln ( 6.2 )}{153.76}) : x = - \frac{W _{- 1} ( - \frac{l n ( 6.2 )}{153.76} ) + 2 ln ( 6.2 )}{ln ( 6.2 )}

解く

(- x - 2) ln (6.2) = W_{0} (- \frac{ln ( 6.2 )}{153.76}) : x = - \frac{W _{0} ( - \frac{l n ( 6.2 )}{153.76} ) + 2 ln ( 6.2 )}{ln ( 6.2 )}

x = - \frac{W _{- 1} ( - \frac{l n ( 6.2 )}{153.76} ) + 2 ln ( 6.2 )}{ln ( 6.2 )}, x = - \frac{W _{0} ( - \frac{l n ( 6.2 )}{153.76} ) + 2 ln ( 6.2 )}{ln ( 6.2 )}

グラフ

人気の例

e^{9 x} = 9 e^{- x}

20 e^{7 k} = 60

45=8(4)^{0.99x}-19

45 = 8 (4)^{0.99 x} - 19

10^7=(10^{-9})(10^x)

1 0^{7} = (1 0^{- 9}) (1 0^{x})

solvefor x,be^{-2x}+3y+3x+11=0

so l v e f or x, b e^{- 2 x} + 3 y + 3 x + 11 = 0