簡約 2ln(3x)+5ln(x-7)-ln(x^2-1)

解

簡約

2 ln (3 x) + 5 ln (x - 7) - ln (x^{2} - 1)

ln (\frac{9 x ^{2} ( x - 7 ) ^{5}}{x ^{2} - 1})

解答ステップ

2 ln (3 x) + 5 ln (x - 7) - ln (x^{2} - 1)

対数の規則を適用する:

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

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

= ln ((3 x)^{2}) + 5 ln (x - 7) - ln (x^{2} - 1)

対数の規則を適用する:

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

5 ln (x - 7) = ln ((x - 7)^{5})

= ln ((3 x)^{2}) + ln ((x - 7)^{5}) - ln (x^{2} - 1)

対数の規則を適用する:

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

ln ((3 x)^{2}) + ln ((x - 7)^{5}) = ln ((3 x)^{2} (x - 7)^{5})

= ln ((3 x)^{2} (x - 7)^{5}) - ln (x^{2} - 1)

簡素化

(3 x)^{2} (x - 7)^{5} : 9 x^{2} (x - 7)^{5}

= ln (9 x^{2} (x - 7)^{5}) - ln (x^{2} - 1)

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 (9 x^{2} (x - 7)^{5}) - ln (x^{2} - 1) = ln (\frac{9 x ^{2} ( x - 7 ) ^{5}}{x ^{2} - 1})

= ln (\frac{9 x ^{2} ( x - 7 ) ^{5}}{x ^{2} - 1})