簡約 2ln(5x^3)+ln(2x^2)

解

簡約

2 ln (5 x^{3}) + ln (2 x^{2})

ln (50 x^{8})

解答ステップ

2 ln (5 x^{3}) + ln (2 x^{2})

対数の規則を適用する:

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

2 ln (5 x^{3}) = ln ((5 x^{3})^{2})

= ln ((5 x^{3})^{2}) + ln (2 x^{2})

対数の規則を適用する:

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

ln ((5 x^{3})^{2}) + ln (2 x^{2}) = ln (2 x^{2} (5 x^{3})^{2})

= ln (2 x^{2} (5 x^{3})^{2})

簡素化

(5 x^{3})^{2} \cdot 2 x^{2} : 50 x^{8}

= ln (50 x^{8})