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

Lösung

vereinfachen

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

ln (\frac{x ^{2} x - 1}{x ^{5} + 3 x ^{4} + 2 x ^{3} - 2 x ^{2} - 3 x - 1})

Schritte zur Lösung

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

Wende die log Regel an:

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

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

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

Wende die log Regel an:

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

4 ln (x + 1) = ln ((x + 1)^{4})

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

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

Wende die log Regel an:

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

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

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

Vereinfache

\frac{\frac{x ^{2}}{( x + 1 ) ^{4}}}{( x - 1 ) ^{\frac{1}{2}}} : \frac{x ^{2} x - 1}{x ^{5} + 3 x ^{4} + 2 x ^{3} - 2 x ^{2} - 3 x - 1}

= ln (\frac{x ^{2} x - 1}{x ^{5} + 3 x ^{4} + 2 x ^{3} - 2 x ^{2} - 3 x - 1})

e x p an d lo g_{5} (\frac{x ^{6}}{y ^{5}})

s im pl i f y 3.5 + lo g_{10} (\frac{0.09949}{0.001})

s im pl i f y 5 ln (3 x - 3) + 2 ln (x - 3)

s im pl i f y 2 (lo g_{6} (x) - 4 lo g_{6} (y)) + 3 lo g_{6} (z)

s im pl i f y - lo g_{10} (3.4 \cdot 1 0^{- 9})