vereinfachen ln|z+4|+6/5 ln((|z-1|)/(|z+4|))+ln|x|

Lösung

vereinfachen

ln ∣ z + 4 ∣ + \frac{6}{5} ln (\frac{∣ z - 1 ∣}{∣ z + 4 ∣}) + ln ∣ x ∣

ln (∣ z + 4 ∣ (\frac{∣ z - 1 ∣}{∣ z + 4 ∣})^{\frac{6}{5}} ∣ x ∣)

Schritte zur Lösung

ln ∣ z + 4 ∣ + \frac{6}{5} ln (\frac{∣ z - 1 ∣}{∣ z + 4 ∣}) + ln ∣ x ∣

Wende die log Regel an:

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

\frac{6}{5} ln (\frac{∣ z - 1 ∣}{∣ z + 4 ∣}) = ln ((\frac{∣ z - 1 ∣}{∣ z + 4 ∣})^{\frac{6}{5}})

= ln ∣ z + 4 ∣ + ln ((\frac{∣ z - 1 ∣}{∣ z + 4 ∣})^{\frac{6}{5}}) + ln ∣ x ∣

Wende die log Regel an:

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

ln ∣ z + 4 ∣ + ln ((\frac{∣ z - 1 ∣}{∣ z + 4 ∣})^{\frac{6}{5}}) = ln ((\frac{∣ z - 1 ∣}{∣ z + 4 ∣})^{\frac{6}{5}} ∣ z + 4 ∣)

= ln (∣ z + 4 ∣ (\frac{∣ z - 1 ∣}{∣ z + 4 ∣})^{\frac{6}{5}}) + ln ∣ x ∣

Wende die log Regel an:

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

ln ((\frac{∣ z - 1 ∣}{∣ z + 4 ∣})^{\frac{6}{5}} ∣ z + 4 ∣) + ln ∣ x ∣ = ln ((\frac{∣ z - 1 ∣}{∣ z + 4 ∣})^{\frac{6}{5}} ∣ x ∣ ∣ z + 4 ∣)

= ln (∣ z + 4 ∣ (\frac{∣ z - 1 ∣}{∣ z + 4 ∣})^{\frac{6}{5}} ∣ x ∣)

s im pl i f y \frac{ln ( 50000000 ) - ln ( 80000000 )}{7 - 4}

e x p an d lo g_{2} (\frac{8}{x + 2})

s im pl i f y lo g_{10} (x) - \frac{1}{3} lo g_{10} (y)

s im pl i f y ln (1 e^{- 0.00018})

j o in 4 lo g_{\frac{5}{3}} (2)