Well your first condition (which should be t>0) would exclude [-12,0] from the domain.
Moreover the third condition should be t<19, so the domain would be (0,19).
In order that "x" be in the domain, all of those functions must be defined so the domain is the intersection of the domains of those individual functions, NOT the union. The domain of ln(7t) is t> 0 (NOT " "- ln(0) is not defined). The domain of requires that and the intersection of those is still t> 0. The domain of is t< 19 (NOT " ! t= 18.999999 is perfectly good.) and the intersection of t> 0 and t< 19 is (0, 19).