vereinfachen ln(((x+1)(x-10))/((x-1)(x+10)))

Lösung

vereinfachen

ln (\frac{( x + 1 ) ( x - 10 )}{( x - 1 ) ( x + 10 )})

ln (x + 1) + ln (x - 10) - ln (x - 1) - ln (x + 10)

Schritte zur Lösung

ln (\frac{( x + 1 ) ( x - 10 )}{( x - 1 ) ( x + 10 )})

Wende die log Regel an:

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

ln (\frac{( x + 1 ) ( x - 10 )}{( x - 1 ) ( x + 10 )}) = ln ((x + 1) (x - 10)) - ln ((x - 1) (x + 10))

= ln ((x + 1) (x - 10)) - ln ((x - 1) (x + 10))

Wende die log Regel an:

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

ln ((x + 1) (x - 10)) = ln (x + 1) + ln (x - 10), ln ((x - 1) (x + 10)) = ln (x - 1) + ln (x + 10)

= ln (x + 1) + ln (x - 10) - (ln (x - 1) + ln (x + 10))

- (ln (x - 1) + ln (x + 10)) : - ln (x - 1) - ln (x + 10)

= ln (x + 1) + ln (x - 10) - ln (x - 1) - ln (x + 10)

s im pl i f y \frac{1}{3} lo g_{3} (5 x)

s im pl i f y 3 lo g_{10} (a) + lo g_{10} (b) - lo g_{10} (c)

s im pl i f y lo g_{10} (\frac{x 3 y ^{5}}{z ^{2}})

s im pl i f y ln (\frac{7 + 41}{4})

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