Sum of all integral values of x satisfying the inequality 3(5/2)log3⁡(12−3x)−3log2⁡x>32

We must have 12 - 3x > 0and x>0 ⇒ x∈(0,4)Therefore, the integral values are 1,2,3.  For x=1;352log3⁡9−3log2⁡1=35−30>32Similarly, x = 2 satisfies but not x= 3 Hence, the required sum = 3.