Slow performance since installing Mavericks

Question

Our Mac is used by four seperate users with their own log in's.  Since installation of Mavericks the performance for two of the users has slowed dramatically to where they get "beachball" for minutes at a time.
The other two users don't experience any slow down at all.
Where do I begin to look for issues and/or ways to speed things up?

Answer 1

Launch the Console application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ Open LaunchPad. Click Utilities, then Console in the icon grid.
The title of the Console window should be All Messages. If it isn't, select
SYSTEM LOG QUERIES ▹ All Messages
from the log list on the left. If you don't see that list, select
View ▹ Show Log List
from the menu bar at the top of the screen.
Click the Clear Display icon in the toolbar. Then try the action that you're having trouble with again. Select any messages that appear in the Console window. Copy them to the Clipboard by pressing the key combination command-C. Paste into a reply to this message by pressing command-V.
☞ The log contains a vast amount of information, almost all of which is irrelevant to solving any particular problem. When posting a log extract, be selective. A few dozen lines are almost always more than enough.
Please don't indiscriminately dump thousands of lines from the log into this discussion.
Please don't post screenshots of log messages—post the text.
☞ Some private information, such as your name, may appear in the log. Anonymize before posting.