vereinfachen-ln(75)-3ln(15/22)

Lösung

vereinfachen

- ln (75) - 3 ln (\frac{15}{22})

- ln (\frac{253125}{10648})

Dezimale

- 3.16851 \dots

Schritte zur Lösung

- ln (75) - 3 ln (\frac{15}{22})

Wende die log Regel an:

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

3 ln (\frac{15}{22}) = ln ((\frac{15}{22})^{3})

= - ln (75) - ln ((\frac{15}{22})^{3})

Schreibe

- ln (75) - ln ((\frac{15}{22})^{3})

um:

- (ln (75) + ln ((\frac{15}{22})^{3}))

= - (ln (75) + ln ((\frac{15}{22})^{3}))

Wende die log Regel an:

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

ln (75) + ln ((\frac{15}{22})^{3}) = ln (75 (\frac{15}{22})^{3})

= - ln (75 (\frac{15}{22})^{3})

75 (\frac{15}{22})^{3} = \frac{253125}{10648}

= - ln (\frac{253125}{10648})

s im pl i f y ln (0.3 e^{4})

s im pl i f y 2 ln (5 x^{3}) + ln (2 x^{2})

s im pl i f y ln (\frac{\frac{1}{2}}{0.144})

s im pl i f y \frac{25 ln ( 3 ) - 9 ln ( 5 )}{8} + 1

j o in \frac{1}{144} ln (2)