vereinfachen ln(ye^{(-x^2-y^2)/2})

Lösung

vereinfachen

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

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

Schritte zur Lösung

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

Wende die log Regel an:

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

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

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

Wende die log Regel an:

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

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

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

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

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

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

j o in 4^{\frac{l n ( \frac{4}{3} )}{3 l n ( 2 )}}

s im pl i f y ln (5 x) + ln (3 x)

s im pl i f y π \cdot ln (\frac{7}{3})

e x p an d lo g_{10} (2 x^{2})