vereinfachen 1/6 [5ln(x+7)-ln(x)-ln(x^2-4)]

Lösung

vereinfachen

\frac{1}{6} [5 ln (x + 7) - ln (x) - ln (x^{2} - 4)]

\frac{1}{6} ln (\frac{( x + 7 ) ^{5}}{x ( x ^{2} - 4 )})

Schritte zur Lösung

\frac{1}{6} [5 ln (x + 7) - ln (x) - ln (x^{2} - 4)]

Wende die log Regel an:

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

5 ln (x + 7) = ln ((x + 7)^{5})

= \frac{1}{6} [ln ((x + 7)^{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 + 7)^{5}) - ln (x) = ln (\frac{( x + 7 ) ^{5}}{x})

= \frac{1}{6} [ln (\frac{( x + 7 ) ^{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 + 7 ) ^{5}}{x}) - ln (x^{2} - 4) = ln (\frac{\frac{( x + 7 ) ^{5}}{x}}{x ^{2} - 4})

= \frac{1}{6} [ln (\frac{\frac{( x + 7 ) ^{5}}{x}}{x ^{2} - 4})]

Wende Bruchregel an:

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

= \frac{1}{6} [ln (\frac{( x + 7 ) ^{5}}{x ( x ^{2} - 4 )})]

Entferne die Klammern:

(a) = a

= \frac{1}{6} ln (\frac{( x + 7 ) ^{5}}{x ( x ^{2} - 4 )})

s im pl i f y ln (\frac{( x - 3 ) ^{2} ( x + 2 ) ^{4}}{( 5 x - 1 ) ^{6}})

s im pl i f y 2 lo g_{10} (x) - \frac{1}{3} lo g_{10} (y)

s im pl i f y \frac{1}{3} ln (\frac{14}{7})

s im pl i f y ln (5) - 2 ln (2)

s im pl i f y 10 ln (\frac{3 x ( x + 2 ) ^{2}}{x + 1})