Question 950484
{{{log(2,(x+2))+log(2,(3-x))=2}}}
{{{log(2,((x+2)(3-x)))=2}}}
{{{(x+2)(3-x)=2^2}}}
{{{3x-x^2+6-2x=4}}}
{{{-x^2+x+6=4}}}
{{{-x^2+x+2=0}}}
{{{x^2-x-2=0}}}
{{{(x-2)(x+1)=0}}}
Two solutions:
{{{x-2=0}}}
{{{x=2}}}
and
{{{x+1=0}}}
{{{x=-1}}}
Verify that these are actually solutions by plugging them into the original equation.