簡約 1/3 ln(6x^2)+ln(3x)

解

簡約

\frac{1}{3} ln (6 x^{2}) + ln (3 x)

ln (336 x 3 x^{2})

解答ステップ

\frac{1}{3} ln (6 x^{2}) + ln (3 x)

対数の規則を適用する:

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

\frac{1}{3} ln (6 x^{2}) = ln ((6 x^{2})^{\frac{1}{3}})

= ln ((6 x^{2})^{\frac{1}{3}}) + ln (3 x)

対数の規則を適用する:

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

ln ((6 x^{2})^{\frac{1}{3}}) + ln (3 x) = ln (3 x (6 x^{2})^{\frac{1}{3}})

= ln (3 x (6 x^{2})^{\frac{1}{3}})

(6 x^{2})^{\frac{1}{3}} = 36 3 x^{2}

= ln (336 x 3 x^{2})