I need to locate a musician
living in the Los Angeles area of California. I need the data base of
the musician's union to accomplish this. He is a guitarist.

Greetings!

In addition to the American Federation of Musicians, local 47, as
mentioned in the comments.  There are a number of other chapters
throughout California.

If you will check with the appropriate local, you can search their
member directory in order to find the musician.

I hope this information assists you in your search.  


Links of interest:

American Federation of Musicians
AFM Locals Serving California
http://www.afm.org/lol.php3



Search terms

musicians union+los angeles

Try the Local 47's search directory:
http://www.promusic47.org/directory/dirheadinclude.asp

Local 47 is the L.A. branch of the American Federation of Musicians.