vereinfachen ln(e^{x^2}(y^2x^2+2xy+(y^4)/2))

Lösung

vereinfachen

ln (e^{x^{2}} (y^{2} x^{2} + 2 x y + \frac{y ^{4}}{2}))

x^{2} + ln (x^{2} y^{2} + 2 x y + \frac{y ^{4}}{2})

Schritte zur Lösung

ln (e^{x^{2}} (y^{2} x^{2} + 2 x y + \frac{y ^{4}}{2}))

Wende die log Regel an:

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

ln (e^{x^{2}} (y^{2} x^{2} + 2 x y + \frac{y ^{4}}{2})) = ln (e^{x^{2}}) + ln (y^{2} x^{2} + 2 x y + \frac{y ^{4}}{2})

= ln (e^{x^{2}}) + ln (\frac{y ^{4}}{2} + x^{2} y^{2} + 2 x y)

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 (y^{2} x^{2} + 2 x y + \frac{y ^{4}}{2})

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

= x^{2} + ln (\frac{y ^{4}}{2} + x^{2} y^{2} + 2 x y)

s im pl i f y - ln (e - 50) + ln (- 50)

s im pl i f y 3 lo g_{2} (x) - 4 lo g_{2} (x + 3)

s im pl i f y ln (0.8) - ln (0.74)

s im pl i f y \frac{1}{10} ln (\frac{0.267 - 0.017}{0.132 - 0.017})

s im pl i f y 4 lo g_{c} (y) - \frac{14}{3} lo g_{c} (x)