erweitern ln(((x^2-x-2)/((x+4)^2))^{1/3})

Lösung

erweitern

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

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

Schritte zur Lösung

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

Wende die log Regel an:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

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

Wende die log Regel an:

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

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

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

Wende die log Regel an:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

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

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