vereinfachen 1/2 (ln(3)-3ln(2)+3ln(1))

Lösung

vereinfachen

\frac{1}{2} (ln (3) - 3 ln (2) + 3 ln (1))

\frac{1}{2} ln (\frac{3}{8})

Dezimale

- 0.49041 \dots

Schritte zur Lösung

\frac{1}{2} (ln (3) - 3 ln (2) + 3 ln (1))

Wende die log Regel an:

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

3 ln (2) = ln (2^{3})

= \frac{1}{2} (3 ln (1) + ln (3) - ln (2^{3}))

Wende die log Regel an:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (3) - ln (2^{3}) = ln (\frac{3}{2 ^{3}})

= \frac{1}{2} (3 ln (1) + ln (\frac{3}{2 ^{3}}))

2^{3} = 8

= \frac{1}{2} (ln (\frac{3}{8}) + 3 ln (1))

3 ln (1) = 0

= \frac{1}{2} (ln (\frac{3}{8}) + 0)

ln (\frac{3}{8}) + 0 = ln (\frac{3}{8})

= \frac{1}{2} ln (\frac{3}{8})

e x p an d lo g_{3} (\frac{y}{9})

e x p an d lo g_{10} ((u v^{5})^{3})

s im pl i f y ln (\frac{30000}{25000})

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

j o in \frac{5 ln ( 3 )}{ln ( \frac{2}{3} )}