vereinfachen ln(x-1)+2ln(x+4)-3ln(x-5)

Lösung

vereinfachen

ln (x - 1) + 2 ln (x + 4) - 3 ln (x - 5)

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

Schritte zur Lösung

ln (x - 1) + 2 ln (x + 4) - 3 ln (x - 5)

Wende die log Regel an:

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

2 ln (x + 4) = ln ((x + 4)^{2})

= ln (x - 1) + ln ((x + 4)^{2}) - 3 ln (x - 5)

Wende die log Regel an:

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

ln (x - 1) + ln ((x + 4)^{2}) = ln ((x + 4)^{2} (x - 1))

= ln ((x - 1) (x + 4)^{2}) - 3 ln (x - 5)

Wende die log Regel an:

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

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

= ln ((x - 1) (x + 4)^{2}) - ln ((x - 5)^{3})

Wende die log Regel an:

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

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

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

f a c t or ln (x^{2} + 3) + 2 ln (x) + C

s im pl i f y 3 lo g_{b} (y) + 7 lo g_{b} (z)

s im pl i f y ln (\frac{1}{23})

s im pl i f y 3 lo g_{b} (z) + 2 (lo g_{b} (y) - 5 lo g_{b} (x))

s im pl i f y - \frac{( 8.314 \cdot 298 )}{96485} ln (\frac{0.002}{4})