vereinfachen 2ln(x)+1/2 ln(x-1)-3ln(x+7)

Lösung

vereinfachen

2 ln (x) + \frac{1}{2} ln (x - 1) - 3 ln (x + 7)

ln (\frac{x ^{2} ( x - 1 ) ^{\frac{1}{2}}}{( x + 7 ) ^{3}})

Schritte zur Lösung

2 ln (x) + \frac{1}{2} ln (x - 1) - 3 ln (x + 7)

Wende die log Regel an:

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

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

= ln (x^{2}) + \frac{1}{2} ln (x - 1) - 3 ln (x + 7)

Wende die log Regel an:

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

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

= ln (x^{2}) + ln ((x - 1)^{\frac{1}{2}}) - 3 ln (x + 7)

Wende die log Regel an:

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

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

= ln (x^{2} (x - 1)^{\frac{1}{2}}) - 3 ln (x + 7)

Wende die log Regel an:

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

3 ln (x + 7) = ln ((x + 7)^{3})

= ln (x^{2} (x - 1)^{\frac{1}{2}}) - ln ((x + 7)^{3})

Wende die log Regel an:

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

ln (x^{2} (x - 1)^{\frac{1}{2}}) - ln ((x + 7)^{3}) = ln (\frac{x ^{2} ( x - 1 ) ^{\frac{1}{2}}}{( x + 7 ) ^{3}})

= ln (\frac{x ^{2} ( x - 1 ) ^{\frac{1}{2}}}{( x + 7 ) ^{3}})

j o in \frac{1}{24} ln cos (3 x^{2})

j o in \frac{1}{3} lo g_{10} (5)

s im pl i f y 0.77 - \frac{8.134 \cdot 298}{1 \cdot 96500} \cdot ln (\frac{1}{4})

s im pl i f y ln (\frac{0.2031}{0.2609})

s im pl i f y \frac{( ln ( z + 4 ) - 6 ln ( z - 1 ) )}{5}