Using the "find -name" command on OS X
Actually you can use the find command as in unix e.g.: find . -name "*.log"

At least on all of my mac systems works this.

see 'man find':

-name pattern
         True if the last component of the pathname being examined matches
         pattern.  Special shell pattern matching characters (``['',
         ``]'', ``*'', and ``?'') may be used as part of pattern.  These
         characters may be matched explicitly by escaping them with a
         backslash (``\'').