vereinfachen ln((\sqrt[3]{x+1})/((3-x)^2(3x-1)))

Lösung

vereinfachen

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

ln (3 x + 1) - 2 ln (3 - x) - ln (3 x - 1)

Schritte zur Lösung

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

Wende die log Regel an:

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

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

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

Wende die log Regel an:

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

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

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

Wende die log Regel an:

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

ln ((3 - x)^{2}) = 2 ln (3 - x)

= ln (3 x + 1) - (2 ln (3 - x) + ln (3 x - 1))

- (2 ln (3 - x) + ln (3 x - 1)) : - 2 ln (3 - x) - ln (3 x - 1)

= ln (3 x + 1) - 2 ln (3 - x) - ln (3 x - 1)

s im pl i f y lo g_{10} (4) + lo g_{10} (5)

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

s im pl i f y 3 lo g_{5} (x) - lo g_{5} (y)

s im pl i f y \frac{1}{3} [2 ln (x + 3) + ln (x) - ln (x^{2} - 1)]

s im pl i f y lo g_{10} (3) + lo g_{10} (2)