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

Lösung

erweitern

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

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

Schritte zur Lösung

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

Wende die log Regel an:

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

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

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

Wende die log Regel an:

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

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

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

Wende die log Regel an:

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

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

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

Wende die log Regel an:

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

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

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

Wende die log Regel an:

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

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

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

- (3 ln (x) + 4 ln (y)) : - 3 ln (x) - 4 ln (y)

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

s im pl i f y 2 [ln (x) - ln (x + 1) - ln (x - 1)]

s im pl i f y lo g_{3} (\frac{x}{5})

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

e x p an d lo g_{5} (\frac{a ^{2} b ^{2} x}{c ^{3}})

s im pl i f y lo g_{3} (5) + lo g_{3} (7)