The parameter m has to be determined for which `4^x-(5m-2)*2^x+4m^2-3m=0` has a unique solution.
let `2^x = y`
For a unique solution `(5m - 2)^2 = 4*(4m^2-3m)`
=> `25m^2 + 4 - 20m = 16m^2 - 12m`
=> `9m^2 - 8m + 4 = 0`
This equation does not have a real solution.
There is no real value of m for which the given equation has a unique solution.