Let

⇒ 3x -1 = A(x-2)(x-3) + B(x-1)(x-3) + C(x-1)(x-2) …(1)

Substituting x = 1, 2 and 3 respectively in equation (1), we get,

A = 1, B = -5 and C = 4

Thus,

= log|x -1| -5log|x-2| + 4log|x-3| + C