vereinfachen ln((x^2\sqrt[3]{x+3})/(\sqrt[4]{z^2-4)})

Lösung

vereinfachen

ln (\frac{x ^{2} 3 x + 3}{4 z ^{2} - 4})

2 ln (x) + ln (3 x + 3) - ln (4 z^{2} - 4)

Schritte zur Lösung

ln (\frac{x ^{2} 3 x + 3}{4 z ^{2} - 4})

Wende die log Regel an:

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

ln (\frac{x ^{2} 3 x + 3}{4 z ^{2} - 4}) = ln (x^{2} 3 x + 3) - ln (4 z^{2} - 4)

= ln (x^{2} 3 x + 3) - ln (4 z^{2} - 4)

Wende die log Regel an:

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

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

= ln (x^{2}) + ln (3 x + 3) - ln (4 z^{2} - 4)

Wende die log Regel an:

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

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

= 2 ln (x) + ln (3 x + 3) - ln (4 z^{2} - 4)

s im pl i f y ln (\frac{1}{3} \cdot \frac{7}{13})

s im pl i f y \frac{( ln ( 85.2 ) - ln ( 115 ) )}{( 2 )}

s im pl i f y ln (\frac{1 0 ^{9}}{( 1.5 )})

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

e x p an d lo g_{4} (\frac{( a ^{2} \cdot b ^{3} )}{c \cdot d})