erweitern ln(sqrt(3r^2s))

Lösung

erweitern

ln (3 r^{2} s)

ln (r) + \frac{1}{2} ln (s) + \frac{1}{2} ln (3)

Schritte zur Lösung

ln (3 r^{2} s)

3 r^{2} s = 3 r s

= ln (3 r s)

Wende die log Regel an:

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

ln (3 r s) = ln (r s) + ln (3)

= ln (r s) + ln (3)

Vereinfache

ln (3) : \frac{1}{2} ln (3)

= ln (r s) + \frac{1}{2} ln (3)

ln (r s) = ln (r) + \frac{1}{2} ln (s)

= ln (r) + \frac{1}{2} ln (s) + \frac{1}{2} ln (3)

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

e x p an d \frac{( 5 cos ( 5 x ) )}{( ( 2 x + 1 ) ^{4} ( 3 x ^{2} - 5 ) ^{3} )}

e x p an d (y sec^{2} (x) + sec (x) tan (x)) d x

e x p an d (x^{2} + 5) d x - (2 y - 1) d y

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