vereinfachen ln((e^x)/(sin(x)(x-2)^2))

Lösung

vereinfachen

ln (\frac{e ^{x}}{sin ( x ) ( x - 2 ) ^{2}})

x - ln (sin (x)) - 2 ln (x - 2)

Schritte zur Lösung

ln (\frac{e ^{x}}{sin ( x ) ( x - 2 ) ^{2}})

Wende die log Regel an:

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

ln (\frac{e ^{x}}{sin ( x ) ( x - 2 ) ^{2}}) = ln (e^{x}) - ln (sin (x) (x - 2)^{2})

= ln (e^{x}) - ln (sin (x) (x - 2)^{2})

Wende die log Regel an:

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

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

= x ln (e) - ln (sin (x) (x - 2)^{2})

Wende die log Regel an:

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

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

= ln (e) x - (ln (sin (x)) + ln ((x - 2)^{2}))

Wende die log Regel an:

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

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

= x ln (e) - (ln (sin (x)) + 2 ln (x - 2))

x ln (e) = x

= x - (ln (sin (x)) + 2 ln (x - 2))

- (ln (sin (x)) + 2 ln (x - 2)) : - ln (sin (x)) - 2 ln (x - 2)

= x - ln (sin (x)) - 2 ln (x - 2)

s im pl i f y ln (\frac{e ^{X^{2}} cos ( X )}{2 X})

s im pl i f y \frac{1}{2} (ln (6) + ln (2))

s im pl i f y lo g_{e} (\frac{( 4300 )}{3})

s im pl i f y ln (\frac{190 ( 200 - 190 )}{3600})

e x p an d lo g_{3} (w^{5} 3 u \cdot v)