vereinfachen ln(a+b)+4ln(a-b)-5ln(c)

Lösung

vereinfachen

ln (a + b) + 4 ln (a - b) - 5 ln (c)

ln (\frac{( a + b ) ( a - b ) ^{4}}{c ^{5}})

Schritte zur Lösung

ln (a + b) + 4 ln (a - b) - 5 ln (c)

Wende die log Regel an:

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

4 ln (a - b) = ln ((a - b)^{4})

= ln (a + b) + ln ((a - b)^{4}) - 5 ln (c)

Wende die log Regel an:

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

ln (a + b) + ln ((a - b)^{4}) = ln ((a - b)^{4} (a + b))

= ln ((a + b) (a - b)^{4}) - 5 ln (c)

Wende die log Regel an:

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

5 ln (c) = ln (c^{5})

= ln ((a + b) (a - b)^{4}) - ln (c^{5})

Wende die log Regel an:

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

ln ((a + b) (a - b)^{4}) - ln (c^{5}) = ln (\frac{( a - b ) ^{4} ( a + b )}{c ^{5}})

= ln (\frac{( a + b ) ( a - b ) ^{4}}{c ^{5}})

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

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

s im pl i f y ln (\frac{1}{298})

s im pl i f y ln (\frac{968.3}{896.5})

j o in \frac{1}{3} lo g_{10} (245)