簡約 5ln|cot(t)|+5ln(1+tan(2)(t))

解

簡約

5 ln ∣ cot (t) ∣ + 5 ln (1 + tan (2) (t))

ln (∣ cot (t) ∣^{5} (1 + tan (2) t)^{5})

解答ステップ

5 ln ∣ cot (t) ∣ + 5 ln (1 + tan (2) (t))

対数の規則を適用する:

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

5 ln ∣ cot (t) ∣ = ln (∣ cot (t) ∣^{5})

= ln (∣ cot (t) ∣^{5}) + 5 ln (tan (2) (t) + 1)

対数の規則を適用する:

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

5 ln (tan (2) (t) + 1) = ln ((tan (2) (t) + 1)^{5})

= ln (∣ cot (t) ∣^{5}) + ln ((tan (2) (t) + 1)^{5})

対数の規則を適用する:

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

ln (∣ cot (t) ∣^{5}) + ln ((1 + tan (2) (t))^{5}) = ln (∣ cot (t) ∣^{5} (tan (2) t + 1)^{5})

= ln (∣ cot (t) ∣^{5} (1 + tan (2) t)^{5})