The number of integral solution x of log x + 7 2 x - 7 2 x - 3 2 ≥ 0 is

Step-by-step solution

We have been given that log x + 7 2 x - 7 2 x - 3 2 ≥ 0 We need to find the domain. For log g x f x is defined when f x > 0 and g x > 0 ,   g x ≠ 1 . ⇒ x + 7 2 > 0 ⇒ x > - 7 2 Also, x + 7 2 ≠ 1 ⇒ x ≠ - 5 2 And x - 7 2 x - 3 ≠ 0 ⇒ x ≠ 7 and x ≠ 3 2 Domain : - 7 2 , ∞ - - 5 2 , 0 , 3 2 Now let us take different cases. Case I: 0 < x + 7 2 < 1 ⇒ - 7 2 < x < - 5 2 . . . . . ( 1 ) ⇒ x - 7 2 x - 3 2 &#8