To solve this equation, we first need to combine the logarithms using the quotient rule.

log4((x+3)/(x-1)) = 2

Now, we can rewrite the equation in exponential form:

4^2 = (x+3)/(x-1)

16 = (x+3)/(x-1)

Next, we can cross multiply to solve for x:

16(x-1) = x + 3

16x - 16 = x + 3

Subtract x from both sides:

15x - 16 = 3

Add 16 to both sides:

15x = 19

Finally, divide by 15 to solve for x:

x = 19/15

Therefore, the solution to the equation Log4(x+3)-log4(x-1)=2 is x = 19/15.