erweitern ln(\sqrt[4]{x^3y^5})

Lösung

erweitern

ln (4 x^{3} y^{5})

ln (y) + \frac{1}{4} ln (x^{3} y)

Schritte zur Lösung

ln (4 x^{3} y^{5})

4 x^{3} y^{5} = y 4 x^{3} y

= ln (y 4 x^{3} y)

Wende die log Regel an:

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

ln (y 4 x^{3} y) = ln (y) + ln (4 x^{3} y)

= ln (y) + ln (4 x^{3} y)

Vereinfache

ln (4 x^{3} y) : \frac{1}{4} ln (x^{3} y)

= ln (y) + \frac{1}{4} ln (x^{3} y)

Vereinfache

ln (x^{3} y) : 3 ln (x) + ln (y)

= ln (y) + \frac{1}{4} (3 ln (x) + ln (y))

ln (y) + 3 ln (x) = ln (y x^{3})

= ln (y) + \frac{1}{4} ln (x^{3} y)

Vereinfache

ln (x^{3} y) : 3 ln (x) + ln (y)

= ln (y) + \frac{1}{4} (3 ln (x) + ln (y))

ln (y) + 3 ln (x) = ln (y x^{3})

= ln (y) + \frac{1}{4} ln (x^{3} y)

e x p an d a (4, - \frac{π}{12})

e x p an d (- \frac{1}{20} (x - 50))^{2}

s im pl i f y (1 + x) (1 - x)

s im pl i f y (x - 1) (x - 1 - 2) (x - 1 + 2)

e x p an d (u - 1)^{2} (u)^{\frac{1}{2}}