The logarithm is defined only when its argument is (strictly) positive. So, you must impose
[tex] x-4>0 [/tex]
Just add 4 to both sides to get
[tex] x > 4 [/tex]
So, the domain is composed by all numbers greater than 4 (excluded), which is represented by the interval
[tex] (4, \infty) [/tex]
