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العربية

vereinfachen 2ln(x-4)-ln(x+4)-ln(x^2-16)+ln(4)+ln(x)

Lösung

vereinfachen

2 ln (x - 4) - ln (x + 4) - ln (x^{2} - 16) + ln (4) + ln (x)

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

Schritte zur Lösung

2 ln (x - 4) - ln (x + 4) - ln (x^{2} - 16) + ln (4) + ln (x)

Wende die log Regel an:

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

2 ln (x - 4) = ln ((x - 4)^{2})

= ln ((x - 4)^{2}) - ln (x + 4) - ln (x^{2} - 16) + ln (4) + ln (x)

Wende die log Regel an:

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

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

= ln (\frac{( x - 4 ) ^{2}}{x + 4}) - ln (x^{2} - 16) + ln (4) + ln (x)

Wende die log Regel an:

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

ln (\frac{( x - 4 ) ^{2}}{x + 4}) - ln (x^{2} - 16) = ln (\frac{\frac{( x - 4 ) ^{2}}{x + 4}}{x ^{2} - 16})

= ln (\frac{\frac{( x - 4 ) ^{2}}{x + 4}}{x ^{2} - 16}) + ln (4) + ln (x)

Vereinfache

\frac{\frac{( x - 4 ) ^{2}}{x + 4}}{x ^{2} - 16} : \frac{x - 4}{( x + 4 ) ^{2}}

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

Wende die log Regel an:

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

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

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

Multipliziere Brüche:

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

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

Wende die log Regel an:

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

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

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

Multipliziere Brüche:

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

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

s im pl i f y ln (x) + ln (y) + \frac{x \frac{d y}{d x} + y}{y}

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