Question 616056
{{{log(x^2-4)-log(x+2)=log(3-x)}}}
{{{log((x^2-4)/(x+2))=log(3-x)}}}
{{{(x^2-4)/(x+2)= 3-x}}}
{{{(x^2-4)= (x+2)(3-x)}}}
{{{x^2-4 = 3x-x^2+6-2x}}}
{{{x^2-4 = x-x^2+6}}}
{{{2x^2-4 = x+6}}}
{{{2x^2-x-4 = 6}}}
{{{2x^2-x-10 = 0}}}
{{{(2x-5)(x+2) = 0}}}
x = {-2, 5/2}
you can throw out the negative solution (extraneous) leaving:
x = 5/2