My macbook air keeps restarting?

Question

My macbook air (2012) keeps restarting. I got the logic board and the battery replaced recently and I tried to update a few days again by restarting and it froze for over 2 hours. I crashed the computer and it was fine. I finished the updates tonight after my computer kept restarting randomly no matter what i was doing and hoped it was from the update but i finished updating and it restarted again about a half hour later. I saw in a post on here to enter
syslog -k Sender kernel -k Message CSeq "Previous Shutdown" | tail | open -f -a TextEdit
in terminal and this is what came up:
Sep 17 07:38:20 Irinas-MacBook-Air kernel[0] <Debug>: Previous Shutdown Cause: 3
--- last message repeated 9 times ---
Sep 22 00:39:19 localhost kernel[0] <Debug>: Previous Shutdown Cause: 3
Sep 22 13:49:24 Irinas-MacBook-Air kernel[0] <Debug>: Previous Shutdown Cause: 3
--- last message repeated 1 time ---
Sep 23 00:58:48 Irinas-MacBook-Air kernel[0] <Debug>: Previous Shutdown Cause: 5
I'm not sure what any of this means but it wasn't negative shutdown causes so im assuming its a different problem than what the person in the other post had (it was said to be hardware/power supply related because of the negative numbers)
I hope this information helps i would like to find an answer from here before going to the apple store since it's not close by to where I live.

Answer 1

If you have more than one user account, you must be logged in as an administrator to carry out these instructions.
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.
Select the most recent panic log under the heading System Diagnostic Reports on the left. If you don't see that heading, select  
View ▹ Show Log List   from the menu bar. Post the entire contents of the panic report — the text, please, not a screenshot. In the interest of privacy, I suggest you edit out the “Anonymous UUID,” a long string of letters, numbers, and dashes in the header and body of the report, if it’s present (it may not be.) Please don't post shutdownStall, spin, or hang reports.