vereinfachen 3/2 ln(x-y)-2ln(x^2+y^2)

Lösung

vereinfachen

\frac{3}{2} ln (x - y) - 2 ln (x^{2} + y^{2})

ln (\frac{( x - y ) ^{\frac{3}{2}}}{( x ^{2} + y ^{2} ) ^{2}})

Schritte zur Lösung

\frac{3}{2} ln (x - y) - 2 ln (x^{2} + y^{2})

Wende die log Regel an:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{3}{2} ln (x - y) = ln ((x - y)^{\frac{3}{2}})

= ln ((x - y)^{\frac{3}{2}}) - 2 ln (x^{2} + y^{2})

Wende die log Regel an:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (x^{2} + y^{2}) = ln ((x^{2} + y^{2})^{2})

= ln ((x - y)^{\frac{3}{2}}) - ln ((x^{2} + y^{2})^{2})

Wende die log Regel an:

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

ln ((x - y)^{\frac{3}{2}}) - ln ((x^{2} + y^{2})^{2}) = ln (\frac{( x - y ) ^{\frac{3}{2}}}{( x ^{2} + y ^{2} ) ^{2}})

= ln (\frac{( x - y ) ^{\frac{3}{2}}}{( x ^{2} + y ^{2} ) ^{2}})

s im pl i f y \frac{9}{8} + \frac{8}{9}

f a c t or x^{2} + x y - 2 y^{2}

f a c t or n + n^{2}

2 x - 4 = 11 - x

f a c t or y^{2 + 2 x y}