vereinfachen 2ln(3)+ln(x)-1/3 ln(x^4+1)

Lösung

vereinfachen

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

ln \frac{9 x ( x ^{4} + 1 ) ^{\frac{2}{3}}}{x ^{4} + 1}

Schritte zur Lösung

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

Wende die log Regel an:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (3) = ln (3^{2})

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

Wende die log Regel an:

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

ln (3^{2}) + ln (x) = ln (3^{2} x)

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

3^{2} = 9

= ln (9 x) - \frac{1}{3} ln (x^{4} + 1)

Wende die log Regel an:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= ln (9 x) - ln ((x^{4} + 1)^{\frac{1}{3}})

Wende die log Regel an:

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

ln (9 x) - ln ((x^{4} + 1)^{\frac{1}{3}}) = ln (\frac{9 x}{( x ^{4} + 1 ) ^{\frac{1}{3}}})

= ln (\frac{9 x}{( x ^{4} + 1 ) ^{\frac{1}{3}}})

Vereinfache

\frac{9 x}{( x ^{4} + 1 ) ^{\frac{1}{3}}} : \frac{9 x ( x ^{4} + 1 ) ^{\frac{2}{3}}}{x ^{4} + 1}

= ln \frac{9 x ( x ^{4} + 1 ) ^{\frac{2}{3}}}{x ^{4} + 1}

s im pl i f y ln (\frac{8}{15})

s im pl i f y lo g_{3} (27 (x - 4)^{3})

s im pl i f y 4 (ln (7) - 2 ln (2)) - \frac{3}{7}

s im pl i f y ln (\frac{2 ^{n}}{( 2 + n ) ^{\frac{3}{4}}})

s im pl i f y - \frac{1}{3} (ln \frac{4}{3} + \frac{2}{3} x - ln - \frac{2}{3} + \frac{2}{3} x)