vereinfachen 5ln|cot(t)|+5ln(1+tan(2)(t))

Lösung

vereinfachen

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

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

Schritte zur Lösung

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

Wende die log Regel an:

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)

Wende die log Regel an:

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})

Wende die log Regel an:

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})

s im pl i f y - lo g_{10} (6.7 \cdot 1 0^{- 4})

e x p an d ln (2 m^{8})

s im pl i f y \frac{1}{11} (lo g_{6} (x) + lo g_{6} (y))

s im pl i f y lo g_{x} (a) - lo g_{x} (b)

s im pl i f y ln (\frac{r}{9 s})