vereinfachen ln((e^3x^3sqrt(x+2))/(3y^2))

Lösung

vereinfachen

ln (\frac{e ^{3} x ^{3} x + 2}{3 y ^{2}})

3 + 3 ln (x) + ln (x + 2) - ln (3) - 2 ln (y)

Schritte zur Lösung

ln (\frac{e ^{3} x ^{3} x + 2}{3 y ^{2}})

Wende die log Regel an:

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

ln (\frac{e ^{3} x ^{3} x + 2}{3 y ^{2}}) = ln (e^{3} x^{3} x + 2) - ln (3 y^{2})

= ln (e^{3} x^{3} x + 2) - ln (3 y^{2})

Wende die log Regel an:

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

ln (e^{3} x^{3} x + 2) = ln (e^{3}) + ln (x^{3}) + ln (x + 2), ln (3 y^{2}) = ln (3) + ln (y^{2})

= ln (e^{3}) + ln (x^{3}) + ln (x + 2) - (ln (y^{2}) + ln (3))

Wende die log Regel an:

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

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

= 3 ln (e) + ln (x^{3}) + ln (x + 2) - (ln (3) + ln (y^{2}))

Wende die log Regel an:

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

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

= 3 ln (e) + 3 ln (x) + ln (x + 2) - (ln (3) + ln (y^{2}))

Wende die log Regel an:

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

ln (y^{2}) = 2 ln (y)

= 3 ln (e) + 3 ln (x) + ln (x + 2) - (ln (3) + 2 ln (y))

3 ln (e) = 3

= 3 + 3 ln (x) + ln (x + 2) - (2 ln (y) + ln (3))

- (ln (3) + 2 ln (y)) : - ln (3) - 2 ln (y)

= 3 + 3 ln (x) + ln (x + 2) - ln (3) - 2 ln (y)

s im pl i f y lo g_{10} (8) - lo g_{10} (2) + 2 lo g_{10} (w)

s im pl i f y ln (\frac{x ^{3}}{7 y ^{2}})

s im pl i f y ln (\frac{1}{0.95})

s im pl i f y ln (\frac{e ^{2} - e ^{4}}{x ^{2} + 7 x + 6})

s im pl i f y lo g_{10} (\frac{3 x ^{3} 4 4 - x}{4 ( x + 4 ) ^{2}})