Step-by-step answer:
The domain of log functions (any legitimate base) requires that the argument evaluates to a positive real number.
For example, the domain of log(4x) will remain positive when x>0.
The domain of log_4(x+3) requires that x+3 >0, i.e. x>-3.
Finally, the domain of log_2(x-3) is such that x-3>0, or x>3.