Question 878678
{{{log(4,(x+3))+log(4,(x-3)) = 2}}}



{{{log(4,((x+3)(x-3))) = 2}}}



{{{(x+3)(x-3) = 4^2}}}



{{{(x+3)(x-3) = 16}}}



{{{x^2-9 = 16}}}



{{{x^2 = 16+9}}}



{{{x^2 = 25}}}



{{{x = ""+-sqrt(25)}}}



{{{x = sqrt(25)}}} or {{{x = -sqrt(25)}}}



{{{x = 5}}} or {{{x = -5}}}



Those are the possible solutions. 
However, only {{{x=5}}} works because {{{x = -5}}} is NOT in the domain of {{{log(4,(x-3))}}}. 
Remember the domain of {{{log(b,(x))}}} is {{{x>0}}} (so the domain of {{{log(4,(x-3))}}} is {{{x>3}}})



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The only solution is {{{x=5}}}