vereinfachen ln(((x^{1/3}))/(x^6sqrt(1+x^2)))

Lösung

vereinfachen

ln \frac{( x ^{\frac{1}{3}} )}{x ^{6} 1 + x ^{2}}

- \frac{17}{3} ln (x) - ln (1 + x^{2})

Schritte zur Lösung

ln \frac{( x ^{\frac{1}{3}} )}{x ^{6} 1 + x ^{2}}

Wende die log Regel an:

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

ln \frac{( x ^{\frac{1}{3}} )}{x ^{6} 1 + x ^{2}} = ln ((x^{\frac{1}{3}})) - ln (x^{6} 1 + x^{2})

= ln (x^{\frac{1}{3}}) - ln (x^{6} x^{2} + 1)

Wende die log Regel an:

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

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

= \frac{1}{3} ln (x) - ln (x^{6} 1 + x^{2})

Wende die log Regel an:

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

ln (x^{6} 1 + x^{2}) = ln (x^{6}) + ln (1 + x^{2})

= \frac{1}{3} ln (x) - (ln (x^{6}) + ln (x^{2} + 1))

Wende die log Regel an:

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

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

= \frac{1}{3} ln (x) - (6 ln (x) + ln (1 + x^{2}))

- (6 ln (x) + ln (1 + x^{2})) : - 6 ln (x) - ln (1 + x^{2})

= \frac{1}{3} ln (x) - 6 ln (x) - ln (1 + x^{2})

Addiere gleiche Elemente:

\frac{1}{3} ln (x) - 6 ln (x) = - \frac{17}{3} ln (x)

= - \frac{17}{3} ln (x) - ln (x^{2} + 1)

s im pl i f y 9.3098 + lo g_{10} (\frac{0.0066}{0.0468})

s im pl i f y ln (\frac{1167}{185})

s im pl i f y ln (\frac{x ^{5}}{y ^{3}}) + ln (\frac{1}{x ^{4} y ^{2}})

j o in \frac{1}{2} ln (2 π + 4 π^{2} + 1)

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