To solve this system of equations, we can use the property of logarithms that states log(a) - log(b) = log(a/b).

From the first two equations, we can rewrite them as:

log2 ((4-x)/(4+x)) = 2
log3 (13+x)/2 = 1

Solving the first equation:
(4-x)/(4+x) = 2^2
(4-x)/(4+x) = 4
4(4+x) = 4 - x
16 + 4x = 4 - x
5x = -12
x = -12/5

Now, substituting x = -12/5 into the second equation:
(13 + (-12/5))/2 = 3
(65 - 12)/10 = 3
53/10 = 3

Therefore, the solution to the system of equations is x = -12/5.