簡約 ln(x^2)-ln(xy^2)+1/2 ln(y^2)

解

簡約

ln (x^{2}) - ln (x y^{2}) + \frac{1}{2} ln (y^{2})

ln (\frac{x}{y})

解答ステップ

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

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

共通因数を約分する:

x

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

対数の規則を適用する:

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

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

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

対数の規則を適用する:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

簡素化

\frac{x}{y ^{2}} (y^{2})^{\frac{1}{2}} : \frac{x}{y}

= ln (\frac{x}{y})