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人気のある代数 >

(ln(x))/x+(4x)^{-1}=0.2

解

\frac{ln ( x )}{x} + (4 x)^{- 1} = 0.2

解

x = - \frac{W _{- 1} ( - \frac{1}{5 e ^{0.25}} )}{0.2}, x = - \frac{W _{0} ( - \frac{1}{5 e ^{0.25}} )}{0.2}

+1

十進法表記

x = 14.68368 \dots, x = 0.93985 \dots

解答ステップ

\frac{ln ( x )}{x} + (4 x)^{- 1} = 0.2

簡素化

\frac{ln ( x )}{x} + (4 x)^{- 1} : \frac{ln ( x )}{x} + \frac{1}{4 x}

\frac{ln ( x )}{x} + \frac{1}{4 x} = 0.2

\frac{1}{4 x}

を右側に移動します

\frac{ln ( x )}{x} = 0.2 - \frac{0.25}{x}

以下で両辺を乗じる:

x

ln (x) = 0.2 x - 0.25

f (x) = g (x)

ならば,

a^{f (x)} = a^{g (x)}

e^{l n (x)} = e^{0.2 x - 0.25}

簡素化

e^{l n (x)} : x

x = e^{0.2 x - 0.25}

解く

x = e^{0.2 x - 0.25} : x = - \frac{W _{- 1} ( - \frac{1}{5 e ^{0.25}} )}{0.2}, x = - \frac{W _{0} ( - \frac{1}{5 e ^{0.25}} )}{0.2}

x = - \frac{W _{- 1} ( - \frac{1}{5 e ^{0.25}} )}{0.2}, x = - \frac{W _{0} ( - \frac{1}{5 e ^{0.25}} )}{0.2}

解を検算する:

x = - \frac{W _{- 1} ( - \frac{1}{5 e ^{0.25}} )}{0.2}

真

, x = - \frac{W _{0} ( - \frac{1}{5 e ^{0.25}} )}{0.2}

真

解答は

x = - \frac{W _{- 1} ( - \frac{1}{5 e ^{0.25}} )}{0.2}, x = - \frac{W _{0} ( - \frac{1}{5 e ^{0.25}} )}{0.2}

グラフ

人気の例

ln(2x-5)-ln(x)= 1/4

ln (2 x - 5) - ln (x) = \frac{1}{4}

29.95=-42.4ln(a)+0.52

29.95 = - 42.4 ln (a) + 0.52

ln(x+2)-ln(6-x)=ln(x-1)

ln (x + 2) - ln (6 - x) = ln (x - 1)

log_{2}(x^9)=-9

lo g_{2} (x^{9}) = - 9

-9log_{2}(8-9x)-5=-41

- 9 lo g_{2} (8 - 9 x) - 5 = - 41