erweitern ln((x(4y-1)^{1/3})^{2/5})

Lösung

erweitern

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

\frac{2}{5} ln (x) + \frac{2}{15} ln (4 y - 1)

Schritte zur Lösung

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

Wende die log Regel an:

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

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

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

Wende die log Regel an:

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

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

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

Wende die log Regel an:

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

ln ((4 y - 1)^{\frac{1}{3}}) = \frac{1}{3} ln (4 y - 1)

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

\frac{2}{5} \cdot \frac{1}{3} ln (4 y - 1) = \frac{2}{15} ln (4 y - 1)

= \frac{2}{5} ln (x) + \frac{2}{15} ln (4 y - 1)

s im pl i f y ln (4 e^{2 x})

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e x p an d lo g_{10} (x^{5}) y^{3}

s im pl i f y lo g_{3} (\frac{p ^{2}}{u w})

e x p an d ln (\frac{a ^{- 2}}{b ^{- 4} c ^{5}})