vereinfachen 3ln(5)-1/2 ln(4)+ln(8)

Lösung

vereinfachen

3 ln (5) - \frac{1}{2} ln (4) + ln (8)

ln (500)

Dezimale

6.21460 \dots

Schritte zur Lösung

3 ln (5) - \frac{1}{2} ln (4) + ln (8)

Wende die log Regel an:

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

3 ln (5) = ln (5^{3})

= ln (5^{3}) - \frac{1}{2} ln (4) + ln (8)

Wende die log Regel an:

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

\frac{1}{2} ln (4) = ln (4^{\frac{1}{2}})

= ln (5^{3}) - ln (4^{\frac{1}{2}}) + ln (8)

Wende die log Regel an:

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

ln (5^{3}) - ln (4^{\frac{1}{2}}) = ln (\frac{5 ^{3}}{4 ^{\frac{1}{2}}})

= ln (\frac{5 ^{3}}{4 ^{\frac{1}{2}}}) + ln (8)

\frac{5 ^{3}}{4 ^{\frac{1}{2}}} = \frac{125}{2}

= ln (\frac{125}{2}) + ln (8)

Wende die log Regel an:

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

ln (\frac{125}{2}) + ln (8) = ln (8 \cdot \frac{125}{2})

= ln (8 \cdot \frac{125}{2})

\frac{125}{2} \cdot 8 = 500

= ln (500)

e x p an d lo g_{4} (\frac{4 a}{b})

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

s im pl i f y ln (\frac{16.9 \cdot 1 0 ^{3}}{80})

s im pl i f y lo g_{3} (sin (x) cos (x))

d o main f (x) = ln^{2} (x) + 2 ln (x) + 1