To solve this equation, we can use the property of logarithms that states:

log_a(b) = log_a(c) if and only if b = c

Therefore, we can set the expressions inside the logarithms equal to each other:

x + 3 = 2x + 9

Now, we can solve for x by rearranging the equation:

x - 2x = 9 - 3
-x = 6

Dividing by -1 on both sides, we get:
x = -6

So, the solution to the equation logx(X+3) = logx(2x+9) is x = -6.