Question 63947
Problem:  3log(X^2)-4log(X^2)+log(2X^3):
If you're the same person I just answered this for, there is more than one way to skin this cat, however you should still come up with the same conclusion.  Doing it your way:
3log(X^2)-4log(X^2)+log(2X^3):
log((X^2)^3)-log((X^2)4)+log(2X^3)
log(X^6)-log(X^8)+log(2X^3)
log(x^6/x^8)+log(2x^3)  because loga-logb=log(a/b)
log(1/x^2)+log(2x^3)  reduce
log((1/x^2)(2x^3))  because loga+logb=log(ab)
log(2x^3/x^2)  
log(2x)  reduce
Happy Calculating!!!