vereinfachen 1/5 ln(y/x+4)+ln(x)

Lösung

vereinfachen

\frac{1}{5} ln (\frac{y}{x} + 4) + ln (x)

ln ((\frac{y + 4 x}{x})^{\frac{1}{5}} x)

Schritte zur Lösung

\frac{1}{5} ln (\frac{y}{x} + 4) + ln (x)

Wende die log Regel an:

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

\frac{1}{5} ln (\frac{y}{x} + 4) = ln ((\frac{y}{x} + 4)^{\frac{1}{5}})

= ln ((\frac{y}{x} + 4)^{\frac{1}{5}}) + ln (x)

Wende die log Regel an:

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

ln ((\frac{y}{x} + 4)^{\frac{1}{5}}) + ln (x) = ln (x (\frac{y}{x} + 4)^{\frac{1}{5}})

= ln (x (\frac{y}{x} + 4)^{\frac{1}{5}})

(\frac{y}{x} + 4)^{\frac{1}{5}} = (\frac{y + 4 x}{x})^{\frac{1}{5}}

= ln ((\frac{y + 4 x}{x})^{\frac{1}{5}} x)

s im pl i f y ln (e^{- x} (x + 0.8))

e x p an d ln ((4 a)^{3})

e x p an d lo g_{5} (\frac{x ^{5}}{y ^{4}})

s im pl i f y 2 ln (2) + \frac{9}{5} ln (4) + \frac{1}{5} ln (- 1)

s im pl i f y lo g_{10} (x) + 4 lo g_{10} (y) - 4 lo g_{10} (z)