vereinfachen 2[2ln(x)-ln(x+4)-ln(x-4)]

Lösung

vereinfachen

2 [2 ln (x) - ln (x + 4) - ln (x - 4)]

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

Schritte zur Lösung

2 [2 ln (x) - ln (x + 4) - ln (x - 4)]

Wende die log Regel an:

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

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

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

Wende die log Regel an:

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

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

= 2 [ln (\frac{x ^{2}}{x + 4}) - ln (x - 4)]

Wende die log Regel an:

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

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

= 2 [ln (\frac{\frac{x ^{2}}{x + 4}}{x - 4})]

Wende Bruchregel an:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= 2 [ln (\frac{x ^{2}}{( x + 4 ) ( x - 4 )})]

Entferne die Klammern:

(a) = a

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

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

s im pl i f y - ln (x^{6}) - ln (y^{6})

s im pl i f y \frac{1}{3} [5 ln (x + 6) + ln (x) - ln (x^{2} - 6)]

s im pl i f y ln (\frac{ln ( e x )}{d})

s im pl i f y - lo g_{10} (5.1 \cdot 1 0^{- 3})