簡約 ln((x^7cos^3(x))/((x-1)^{9/2)})

解

簡約

ln (\frac{x ^{7} cos ^{3} ( x )}{( x - 1 ) ^{\frac{9}{2}}})

7 ln (x) + ln (cos^{3} (x)) - \frac{9}{2} ln (x - 1)

解答ステップ

ln (\frac{x ^{7} cos ^{3} ( x )}{( x - 1 ) ^{\frac{9}{2}}})

対数の規則を適用する:

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

ln (\frac{x ^{7} cos ^{3} ( x )}{( x - 1 ) ^{\frac{9}{2}}}) = ln (x^{7} cos^{3} (x)) - ln ((x - 1)^{\frac{9}{2}})

= ln (x^{7} cos^{3} (x)) - ln ((x - 1)^{\frac{9}{2}})

対数の規則を適用する:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= ln (x^{7} cos^{3} (x)) - \frac{9}{2} ln (x - 1)

対数の規則を適用する:

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

ln (x^{7} cos^{3} (x)) = ln (x^{7}) + ln (cos^{3} (x))

= ln (x^{7}) + ln (cos^{3} (x)) - \frac{9}{2} ln (x - 1)

対数の規則を適用する:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= 7 ln (x) + ln (cos^{3} (x)) - \frac{9}{2} ln (x - 1)