vereinfachen 1/2 ln(2(7)+1)+2ln(7-1)+c

Lösung

vereinfachen

\frac{1}{2} ln (2 (7) + 1) + 2 ln (7 - 1) + c

ln (36 \cdot 1 5^{\frac{1}{2}}) + c

Schritte zur Lösung

\frac{1}{2} ln (2 (7) + 1) + 2 ln (7 - 1) + c

Wende die log Regel an:

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

\frac{1}{2} ln (2 (7) + 1) = ln ((2 (7) + 1)^{\frac{1}{2}})

= ln ((2 (7) + 1)^{\frac{1}{2}}) + 2 ln (7 - 1) + c

Wende die log Regel an:

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

2 ln (7 - 1) = ln ((7 - 1)^{2})

= ln ((2 (7) + 1)^{\frac{1}{2}}) + ln ((7 - 1)^{2}) + c

Wende die log Regel an:

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

ln ((2 (7) + 1)^{\frac{1}{2}}) + ln ((7 - 1)^{2}) = ln ((7 - 1)^{2} (2 \cdot 7 + 1)^{\frac{1}{2}})

= ln ((7 - 1)^{2} (2 \cdot 7 + 1)^{\frac{1}{2}}) + c

(2 (7) + 1)^{\frac{1}{2}} (7 - 1)^{2} = 36 \cdot 1 5^{\frac{1}{2}}

= ln (36 \cdot 1 5^{\frac{1}{2}}) + c

s im pl i f y (3 lo g_{10} (x) + 2 lo g_{10} (y)) - 6 lo g_{10} (z)

s im pl i f y 2 ln (x + 13) - ln (x + 7)

e x p an d lo g_{10} (\frac{2 x}{y})

s im pl i f y 3 lo g_{c} (x + 3) (lo g_{c} (z) - 4 lo g_{c} (y))

s im pl i f y ln (7) - 2 (ln (4) + ln (32))