vereinfachen 1/6 [5ln(x+9)-ln(x)-ln(x^2-4)]

Lösung

vereinfachen

\frac{1}{6} [5 ln (x + 9) - ln (x) - ln (x^{2} - 4)]

\frac{1}{6} ln (\frac{( x + 9 ) ^{5}}{x ( x ^{2} - 4 )})

Schritte zur Lösung

\frac{1}{6} [5 ln (x + 9) - ln (x) - ln (x^{2} - 4)]

Wende die log Regel an:

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

5 ln (x + 9) = ln ((x + 9)^{5})

= \frac{1}{6} [ln ((x + 9)^{5}) - ln (x) - ln (x^{2} - 4)]

Wende die log Regel an:

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

ln ((x + 9)^{5}) - ln (x) = ln (\frac{( x + 9 ) ^{5}}{x})

= \frac{1}{6} [ln (\frac{( x + 9 ) ^{5}}{x}) - ln (x^{2} - 4)]

Wende die log Regel an:

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

ln (\frac{( x + 9 ) ^{5}}{x}) - ln (x^{2} - 4) = ln (\frac{\frac{( x + 9 ) ^{5}}{x}}{x ^{2} - 4})

= \frac{1}{6} [ln (\frac{\frac{( x + 9 ) ^{5}}{x}}{x ^{2} - 4})]

Wende Bruchregel an:

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

= \frac{1}{6} [ln (\frac{( x + 9 ) ^{5}}{x ( x ^{2} - 4 )})]

Entferne die Klammern:

(a) = a

= \frac{1}{6} ln (\frac{( x + 9 ) ^{5}}{x ( x ^{2} - 4 )})

s im pl i f y \frac{1}{3} (ln (5) - ln (7))

s im pl i f y 3 ln ∣ x ∣ - 4 ln ∣ x + 1 ∣

s im pl i f y ln ((4 x^{(2)} - 5) (2 x - 5)^{(3)})

s im pl i f y \frac{1}{- 0.03794} ln (\frac{1}{76})

s im pl i f y ln (x y) - 3