vereinfachen 1/3 ln(x)+4[ln(x-3)-3/8 ln(x+3)]

Lösung

vereinfachen

\frac{1}{3} ln (x) + 4 [ln (x - 3) - \frac{3}{8} ln (x + 3)]

\frac{1}{3} ln (x) + 4 ln (\frac{( x - 3 ) ( x + 3 ) ^{\frac{5}{8}}}{x + 3})

Schritte zur Lösung

\frac{1}{3} ln (x) + 4 [ln (x - 3) - \frac{3}{8} ln (x + 3)]

Wende die log Regel an:

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

\frac{3}{8} ln (x + 3) = ln ((x + 3)^{\frac{3}{8}})

= \frac{1}{3} ln (x) + 4 [ln (x - 3) - ln ((x + 3)^{\frac{3}{8}})]

Wende die log Regel an:

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

ln (x - 3) - ln ((x + 3)^{\frac{3}{8}}) = ln (\frac{x - 3}{( x + 3 ) ^{\frac{3}{8}}})

= \frac{1}{3} ln (x) + 4 [ln (\frac{x - 3}{( x + 3 ) ^{\frac{3}{8}}})]

Vereinfache

\frac{x - 3}{( x + 3 ) ^{\frac{3}{8}}} : \frac{( x - 3 ) ( x + 3 ) ^{\frac{5}{8}}}{x + 3}

= \frac{1}{3} ln (x) + 4 [ln (\frac{( x - 3 ) ( x + 3 ) ^{\frac{5}{8}}}{x + 3})]

Entferne die Klammern:

(a) = a

= \frac{1}{3} ln (x) + 4 ln (\frac{( x - 3 ) ( x + 3 ) ^{\frac{5}{8}}}{x + 3})

s im pl i f y ln (a + b) + ln (a - b) - 9 ln (c)

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

s im pl i f y 4 [ln (z) + ln (z + 5)] - 2 ln (z - 5)

s im pl i f y ln (x^{2} y)

s im pl i f y lo g_{5} (\frac{14 x}{y})