Number of integral solutions of inequality 1 10 log x - 3 ⁡ x 2 - 4 x + 3 ≥ 1 are

Step-by-step solution

1 10 log x - 3 ⁡ x 2 - 4 x + 3 ≥ 1 10 0 ⇒ log x - 3 ⁡ x 2 - 4 x + 3 ≤ 0 (base is less than 1) Case - I : x - 3 > 1 and 0 < x 2 - 4 x + 3 ≤ 1 ⇒ x > 4 and ( x - 1 ) ( x - 3 ) > 0 and x 2 - 4 x + 2 ≤ 0 ⇒ x > 4 and x 2 - 4 x + 2 ≤ 0 ⇒ x > 4 and 2 - 2 ≤ x ≤ 2 + 2 ∴ not possible ∴ No Solution Case - II : 0 < x - 3 < 1 and x 2 - 4 x + 3 ≥ 1 ⇒ 3 < x < 4 and x ≤ 2 - 2 x ≥ 2 + 2 ⇒ 2 + 2 ≤ x < 4 ⇒ there is no integral value of x.