Using the properties of logarithms, we can simplify the given equation:

Log3((3x-1)(1+x)) = 1 + log3(x+3)

Log3(3x^2 + 3x - x - 1) = 1 + log3(x+3)

Log3(3x^2 + 2x - 1) = 1 + log3(x+3)

Taking the antilogarithm of both sides:

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

3x^2 + 2x - 1 = 3x + 9

3x^2 - x - 10 = 0

(3x + 5)(x - 2) = 0

Therefore, x = -5/3 or x = 2.