log(2,x)+log(1/2,(x+1))>log(2,(x-2)).......change to base 10
log(x)/log(2)+log(x+1)/log(1/2)>log(x-2)/log(2).....since log(1/2)=log(1)-log(2)=0-log(2)=log(2) we have
log(x)/log(2)-log(x+1)/log(2)>log(x-2)/log(2).........since all denominators same
log(x)-log(x+1)>log(x-2)
log(x/(x+1))-log(x-2)>0
log((x/(x+1))/(x-2))>0
log(x/(x^2 - x - 2))>0
(x^2 - 2x - 2)/((x - 2) (x + 1))<0
Real solutions:
-1<x<1 - sqrt(3)
2<x<1 + sqrt(3)
