For y = log _b (a) to be well-defined, the value of a must be a > 0 and b > 0, b <> 1.

y = log _x+4 (3-2x) to be well-defined,

3-2x > 0

=> -2x > -3

=> 2x < 3

=> x < 1.5

x+4 > 1

=> x >  -3

Hence  -3 < x < 1.5