How can I join boards for table legs?
There is a way to create such a composite timber. Actually, all other things being equal (the species, cut and quality of the wood), a built up sandwich is actually stronger than a solid piece of wood. 

This is done by laminating the three boards together. A generous layer of wood glue, such as Titebond II, is spread over one face of one of the boards. The next board is placed over this and a second spread of glue is placed on the face of board 2. Finally board three is placed on top.

The boards are aligned and clamped in numerous places along their length. If you are able to clamp them to a very firm perfectly flat surface (such as the platform of a table saw) even better.  You need to make sure that there is no bow or twist in the clamped boards.

Once the glue dries (at least 24 hours) you can then trim the ends.

The newel post on the stair rail shown in this question and answer is made up from 3 1x3 oak boards laminated in the manner described. 

Unless the table will bear an extremely heavy load or the taper is very extreme (or the wood you are using is balsa), a laminated 2.5 inch leg should be more than sufficient.