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人気のある代数 >

8ln(x^2)=x

解

8 ln (x^{2}) = x

解

x = - 16 W_{0} (\frac{1}{16}), x = - 16 W_{0} (- \frac{1}{16}), x = - 16 W_{- 1} (- \frac{1}{16})

+1

十進法表記

x = - 0.94277 \dots, x = 1.06910 \dots, x = 67.36107 \dots

解答ステップ

8 ln (x^{2}) = x

以下で両辺を割る

8

ln (x^{2}) = \frac{x}{8}

f (x) = g (x)

ならば,

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

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

簡素化

e^{l n (x^{2})} : x^{2}

x^{2} = e^{\frac{x}{8}}

解く

x^{2} = e^{\frac{x}{8}} : x = - 16 W_{0} (\frac{1}{16}), x = - 16 W_{0} (- \frac{1}{16}), x = - 16 W_{- 1} (- \frac{1}{16})

x = - 16 W_{0} (\frac{1}{16}), x = - 16 W_{0} (- \frac{1}{16}), x = - 16 W_{- 1} (- \frac{1}{16})

解を検算する:

x = - 16 W_{0} (\frac{1}{16})

真

, x = - 16 W_{0} (- \frac{1}{16})

真

, x = - 16 W_{- 1} (- \frac{1}{16})

真

解答は

x = - 16 W_{0} (\frac{1}{16}), x = - 16 W_{0} (- \frac{1}{16}), x = - 16 W_{- 1} (- \frac{1}{16})

グラフ

人気の例

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

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

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lo g_{3} (3 x - 1) - lo g_{3} (2 x + 3) = 1 + lo g_{3} (x)

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