The values of 'a' for which `4^x-(a-4) 2^x+(9a)/4<0 AAx in(1,2)` is

Explanation

Let `2^x=t` in which `t in(2, 4)`.
And we have to find the values of `a` which `f(t) = t^(2) - (a - 4)t + (9/4) alt 0` for all `t in(2, 4)`
Since coefficient of `t^(2)` is positive, graph of `f(t)` is concave upward.
So, for given condition,
`f(2) lt 0` and `f(4)lt0`
because `4 - (a-4)2+(9/4)a lt 0` and `16- (a-4)4 + (9/4)a lt0`
because `a lt - 48` and `a gt 128/7`
Clearly, no common value of a exists.
Hence, no such `a` exists.