In the given equation the right hand side contains the powers of 2 and 3 only; therefore the left hand side should contain the powers of 2 and 3 only. Since (x - 1)(x - 2)(x - 3) is a product of three consecutive numbers, it will always contain either one or two multiples of 2 and one multiple o f 3. Lets make two cases: (1) If (x - 1) and (x - 3) are multiples of 2. Let (x - 1) be equal to 2k; then (x - 3) is equal to 2(k + 1). Now k and (k + 1) should both contain powers of 2 or 3 only. This is possible with k = 1, 2 or 3. Also if any of k or (k + 1) is a multiple of 3, (x - 2) will not be a multiple of 3 or 2. So again it will not satisfy. (2) If (x - 2) is a multiple of 2: Here (x - 1) and (x - 3) will both be odd, out of which only one will be a multiple of 3. Hence the other number will be a multiple of an odd number other than 3. So the equation can be satisfied only if that other odd number is 1. Hence taking one odd number as 1 we get 1 × 2 × 3 which is equal to 6. Hence the equation is satisfied for x = 4 only.