Final answer:
Na3PO4 would be most soluble in a basic solution due to the presence of a weak acid conjugate base.
Step-by-step explanation:
The salt that would be most soluble in a basic solution is Na3PO4.
When Na3PO4 dissolves in water, it forms 3 Na+ ions and 1 PO4^3- ion. The Na+ ions are the conjugate acid of a strong base, which does not affect the pH of the solution. However, the PO4^3- ion is the conjugate base of a weak acid, which makes the solution basic.
In contrast, the other salts listed in the options (BaSO4, KBrd, LiCl, NH4Br) are either insoluble or the conjugate base of a strong acid, which would not make the solution basic.