vereinfachen ln((e^{X^2}cos(X))/(sqrt(2X)))

Lösung

vereinfachen

ln (\frac{e ^{X^{2}} cos ( X )}{2 X})

X^{2} + ln (cos (X)) - ln (2 X)

Schritte zur Lösung

ln (\frac{e ^{X^{2}} cos ( X )}{2 X})

Wende die log Regel an:

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

ln (\frac{e ^{X^{2}} cos ( X )}{2 X}) = ln (e^{X^{2}} cos (X)) - ln (2 X)

= ln (e^{X^{2}} cos (X)) - ln (2 X)

Wende die log Regel an:

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

ln (e^{X^{2}} cos (X)) = ln (e^{X^{2}}) + ln (cos (X))

= ln (e^{X^{2}}) + ln (cos (X)) - ln (2 X)

Wende die log Regel an:

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

ln (e^{X^{2}}) = X^{2} ln (e)

= X^{2} ln (e) + ln (cos (X)) - ln (2 X)

X^{2} ln (e) = X^{2}

ln (2 X) = ln (2 X)

= X^{2} + ln (cos (X)) - ln (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)

e x p an d \frac{1}{2} ln (6) + \frac{1}{2} ln (x) - \frac{1}{2} ln (x - 6)