How do you solve ln(x^2-x+1)-ln(x-1)+ln(x^2-1)=ln9ln(x2−x+1)−ln(x−1)+ln(x2−1)=ln9?

1 Answer
cspark1981
Nov 1, 2015

x = 2 x=2

Explanation:

ln A + ln B = ln (AB) lnA+lnB=ln(AB)
ln A - ln B = ln (A/B) lnA−lnB=ln(AB)

ln (x^2-x+1) - ln (x−1) + ln (x^2−1) = ln 9 ln(x2−x+1)−ln(x−1)+ln(x2−1)=ln9
ln (((x^2-x+1)(x^2−1))/(x−1)) = ln 9 ln((x2−x+1)(x2−1)x−1)=ln9
ln (((x^2-x+1)(x−1)(x+1))/(x−1)) = ln 9 ln((x2−x+1)(x−1)(x+1)x−1)=ln9
(x^2-x+1)(x+1) = 9 (x2−x+1)(x+1)=9
x^3 = 8 x3=8
x = 2 x=2

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