The least positive onteger for which x `4^(x)+8^((2//3)(x-2))-72-4^(x-3//2)` is non-negative, is

Explanation

We have,
`4^(x)+8^(2//3(x-2))-72-4^(x-3//2)ge0`
`rArr 2^(2x)+2^(2x-4)-2^(2x-3)-72 ge 0`
`rArr 2^(2x)+(2^(2x))/(16)-(2^(2x))/(8)-72 ge 0 rArr2^(2x-4)ge (24)/(5)`
Clearly, 4 is the smallest positive integer satisfying this inequation.