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

Lösung

vereinfachen

ln (\frac{x ^{2}}{e ^{x c o s (x)}})

2 ln (x) - x cos (x)

Schritte zur Lösung

ln (\frac{x ^{2}}{e ^{x c o s (x)}})

Wende die log Regel an:

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

ln (\frac{x ^{2}}{e ^{x c o s (x)}}) = ln (x^{2}) - ln (e^{x c o s (x)})

= ln (x^{2}) - ln (e^{x c o s (x)})

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 (e^{x c o s (x)})

Wende die log Regel an:

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

ln (e^{x c o s (x)}) = x cos (x) ln (e)

= 2 ln (x) - x cos (x) ln (e)

x cos (x) ln (e) = x cos (x)

= 2 ln (x) - x cos (x)

e x p an d lo g_{8} (\frac{x ^{3}}{5})

s im pl i f y - \frac{1}{3} + \frac{1}{3} ln (\frac{3 + 5}{2})

s im pl i f y 3 ln (2) - 2 ln (3)

s im pl i f y \frac{6 ln ( 3 ) - 10 ln ( 2 )}{2}

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