Question 865315
{{{log((x^2+x-6))-log((x^2-9))}}}



{{{log(((x^2+x-6)/(x^2-9)))}}} Use rule 2 from <a href="http://www.purplemath.com/modules/logrules.htm">this page</a>



{{{log((((x+3)(x-2))/(x^2-9)))}}} Factor the numerator



{{{log((((x+3)(x-2))/((x-3)(x+3))))}}} Factor the denominator



{{{log(((highlight((x+3))(x-2))/((x-3)highlight((x+3)))))}}} Highlight common terms



{{{log(((cross((x+3))(x-2))/((x-3)cross((x+3)))))}}} Cancel out those common terms (they divide to 1 and go away, since 1*any number = any number)



{{{log(((x-2)/(x-3)))}}} 



===================================================================



So {{{log((x^2+x-6))-log((x^2-9))}}} simplifies to {{{log(((x-2)/(x-3)))}}}