vereinfachen ln(5)+1/5 ln(4-x^2)-ln(x)

Lösung

vereinfachen

ln (5) + \frac{1}{5} ln (4 - x^{2}) - ln (x)

ln \frac{5 ( 4 - x ^{2} ) ^{\frac{1}{5}}}{x}

Schritte zur Lösung

ln (5) + \frac{1}{5} ln (4 - x^{2}) - ln (x)

Wende die log Regel an:

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

\frac{1}{5} ln (- x^{2} + 4) = ln ((- x^{2} + 4)^{\frac{1}{5}})

= ln (5) + ln ((- x^{2} + 4)^{\frac{1}{5}}) - ln (x)

Wende die log Regel an:

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

ln (5) + ln ((4 - x^{2})^{\frac{1}{5}}) = ln (5 (- x^{2} + 4)^{\frac{1}{5}})

= ln (5 (4 - x^{2})^{\frac{1}{5}}) - ln (x)

Wende die log Regel an:

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

ln (5 (4 - x^{2})^{\frac{1}{5}}) - ln (x) = ln \frac{5 ( - x ^{2} + 4 ) ^{\frac{1}{5}}}{x}

= ln \frac{5 ( 4 - x ^{2} ) ^{\frac{1}{5}}}{x}

s im pl i f y - lo g_{10} (3 x 1 0^{- 5})

j o in \frac{5 ln ( 2 )}{ln ( \frac{533}{500} )}

s im pl i f y ln (\frac{8}{8 + 4})

s im pl i f y ln (6) - 2 ln (2)

s im pl i f y \frac{d}{d x} (\frac{1}{ln ( x ^{2} )}) - ln (\frac{1}{x ^{2}})