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

Lösung

vereinfachen

- ln (x) + 2 ln (x + 1) + 2 ln (x - 1)

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

Schritte zur Lösung

- ln (x) + 2 ln (x + 1) + 2 ln (x - 1)

Wende die log Regel an:

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

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

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

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

Wende die log Regel an:

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

2 ln (x - 1) = ln ((x - 1)^{2})

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

Wende die log Regel an:

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

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

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

Multipliziere Brüche:

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

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

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