vereinfachen-1/2 ln(y/x)-ln(x)

Lösung

vereinfachen

- \frac{1}{2} ln (\frac{y}{x}) - ln (x)

- ln ((\frac{y}{x})^{\frac{1}{2}} x)

Schritte zur Lösung

- \frac{1}{2} ln (\frac{y}{x}) - ln (x)

Wende die log Regel an:

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

\frac{1}{2} ln (\frac{y}{x}) = ln ((\frac{y}{x})^{\frac{1}{2}})

= - ln ((\frac{y}{x})^{\frac{1}{2}}) - ln (x)

Schreibe

- ln ((\frac{y}{x})^{\frac{1}{2}}) - ln (x)

um:

- (ln ((\frac{y}{x})^{\frac{1}{2}}) + ln (x))

= - (ln ((\frac{y}{x})^{\frac{1}{2}}) + ln (x))

Wende die log Regel an:

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

ln ((\frac{y}{x})^{\frac{1}{2}}) + ln (x) = ln ((\frac{y}{x})^{\frac{1}{2}} x)

= - ln ((\frac{y}{x})^{\frac{1}{2}} x)

s im pl i f y ln (2 (\frac{1}{9})^{2}) - 18 \cdot \frac{1}{9}

s im pl i f y 5 lo g_{e} (2) + 7 lo g_{e} (x) + 4 lo g_{e} (y)

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

s im pl i f y ln (x - 1) - ln (x + 2)

f a c t or ln ∣ y ∣ - \frac{1}{2} ln y^{2} + 1 + C