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

Lösung

vereinfachen

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

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

Schritte zur Lösung

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

Wende die log Regel an:

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

ln (x) - ln (x - 4) = ln (\frac{x}{x - 4})

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

Wende die log Regel an:

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

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

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

Wende die log Regel an:

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

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

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

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

s im pl i f y \frac{1}{2} ln (x) + 6 ln (y) - 9 ln (z)

s im pl i f y lo g_{10} (\frac{- 5 ^{7} 2 ^{5}}{- 1 0 ^{8}})

s im pl i f y lo g_{b} (u^{5} v^{2})

s im pl i f y - ln (x) + ln (c)

s im pl i f y \frac{1}{3} lo g_{c} (x) + 4 lo g_{c} (y) - 3 lo g_{c} (x)