Question 691108
exact value for the solution of the equation.
log(x^2+4)-log(x+2) = 2+log(x-2)
subtracting indicates divide so we can write it
{{{log(((x^2+4)/(x+2)))}}} = 2 + log(x-2)
Subtract log(x-2) from both sides
{{{log(((x^2+4)/(x+2)))}}} - log(x-2) = 2
which we can combine
{{{log(((x^2+4)/((x+2)(x-2))))}}} = 2 
which is
{{{log(((x^2+4)/(x^2-4)))}}} = 2
find the antilog (10^x) of both sides (10^2 = 100)
{{{((x^2+4)/(x^2-4))}}} = 100
multiply both sides by x^2-4
{{{x^2 + 4 = 100(x^2-4)}}}
{{{x^2 + 4 = 100x^2-400}}}
combine like terms
0 = 100x^2 - x^2  - 400 - 4 
99x^2 - 404 = 0
99x^2 = 404
x^2 = {{{404/99}}}
x = {{{sqrt(404/99)}}}
x = {{{sqrt((4*101)/(9*11))}}}
Extract the square roots of the perfect squares
x ={{{2/3}}}*{{{sqrt(101/11)}}}
x ~  2.02