簡約 x(ln^2(x)-2ln(x))

解

簡約

x (ln^{2} (x) - 2 ln (x))

x ln^{2} (x)

解答ステップ

x (ln^{2} (x) - 2 ln (x))

対数の規則を適用する:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

対数の規則を適用する:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

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

共通因数を約分する:

x

= x ln^{2} (\frac{1}{x})

ln^{2} (\frac{1}{x}) = ln^{2} (x)

= x ln^{2} (x)