vereinfachen 1/2 [ln(x+1)+2ln(x-1)]+3ln(x)

Lösung

vereinfachen

\frac{1}{2} [ln (x + 1) + 2 ln (x - 1)] + 3 ln (x)

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

Schritte zur Lösung

\frac{1}{2} [ln (x + 1) + 2 ln (x - 1)] + 3 ln (x)

Wende die log Regel an:

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

2 ln (x - 1) = ln ((x - 1)^{2})

= \frac{1}{2} [ln (x + 1) + ln ((x - 1)^{2})] + 3 ln (x)

Wende die log Regel an:

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

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

= \frac{1}{2} [ln ((x + 1) (x - 1)^{2})] + 3 ln (x)

Entferne die Klammern:

(a) = a

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

s im pl i f y ln ((e^{3}) \cdot (x^{3}) \cdot (y^{4}))

s im pl i f y \frac{5}{4} ln (x) - \frac{7}{2 x} - \frac{5}{4} ln (x + 2) + C

e x p an d lo g_{10} ((tan (x))^{\circ}) 2 x

s im pl i f y 2 lo g_{10} (x) - 5 lo g_{10} (x - 1)

s im pl i f y ln (\frac{3}{2}) + 1