erweitern ln(\sqrt[5]{(yz)/(x^6)})

Lösung

erweitern

ln (5 \frac{yz}{x ^{6}})

\frac{1}{5} ln (yz) - \frac{6}{5} ln (x)

Schritte zur Lösung

ln (5 \frac{yz}{x ^{6}})

Schreibe um

= ln ((\frac{yz}{x ^{6}})^{\frac{1}{5}})

Wende log Regel an

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

angenommen

x \geq 0

= \frac{1}{5} ln (\frac{yz}{x ^{6}})

Vereinfache

ln (\frac{yz}{x ^{6}}) : - 6 ln (x) + ln (yz)

= \frac{1}{5} (- 6 ln (x) + ln (yz))

Wende das Distributivgesetz an:

a (b - c) = ab - a c

a = \frac{1}{5}, b = ln (yz), c = 6 ln (x)

= \frac{1}{5} ln (yz) - \frac{1}{5} \cdot 6 ln (x)

= \frac{1}{5} ln (yz) - 6 \cdot \frac{1}{5} ln (x)

6 \cdot \frac{1}{5} ln (x) = \frac{6}{5} ln (x)

= \frac{1}{5} ln (yz) - \frac{6}{5} ln (x)

e x p an d \frac{x ^{4} + 5 x ^{2} + 2}{x ^{2} ( x ^{2} + 1 ) ^{2}}

e x p an d \frac{( x - 18 )}{( x + 1 ) ( x - 5 )}

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

e x p an d \frac{1 - x + 3}{( x + 2 ) ^{2}}

e x p an d (t + e^{- 2 t})^{2}