vereinfachen ln(((\sqrt[3]{x^2})y^6)/(w^3z^4))

Lösung

vereinfachen

ln \frac{( 3 x ^{2} ) y ^{6}}{w ^{3} z ^{4}}

ln (3 x^{2}) + 6 ln (y) - 3 ln (w) - 4 ln (z)

Schritte zur Lösung

ln \frac{( 3 x ^{2} ) y ^{6}}{w ^{3} z ^{4}}

Wende die log Regel an:

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

ln \frac{( 3 x ^{2} ) y ^{6}}{w ^{3} z ^{4}} = ln ((3 x^{2}) y^{6}) - ln (w^{3} z^{4})

= ln (y^{6} 3 x^{2}) - ln (w^{3} z^{4})

Wende die log Regel an:

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

ln (3 x^{2} y^{6}) = ln (3 x^{2}) + ln (y^{6}), ln (w^{3} z^{4}) = ln (w^{3}) + ln (z^{4})

= ln (3 x^{2}) + ln (y^{6}) - (ln (w^{3}) + ln (z^{4}))

Wende die log Regel an:

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

ln (y^{6}) = 6 ln (y)

= ln (3 x^{2}) + 6 ln (y) - (ln (w^{3}) + ln (z^{4}))

Wende die log Regel an:

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

ln (w^{3}) = 3 ln (w)

= ln (3 x^{2}) + 6 ln (y) - (3 ln (w) + ln (z^{4}))

Wende die log Regel an:

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

ln (z^{4}) = 4 ln (z)

= ln (3 x^{2}) + 6 ln (y) - (3 ln (w) + 4 ln (z))

- (3 ln (w) + 4 ln (z)) : - 3 ln (w) - 4 ln (z)

= ln (3 x^{2}) + 6 ln (y) - 3 ln (w) - 4 ln (z)

e x p an d lo g_{8} (\frac{64}{x + 1})

s im pl i f y 9 ln (a) - 6 ln (b)

s im pl i f y 2 lo g_{10} (2) + 2 lo g_{10} (3)

s im pl i f y 2 ln (x) + 5 ln (y) - 6 ln (z)

s im pl i f y x ln (2) + 5 ln (x - 1) - 2 ln (x + 3)