You can find the client log files here:
- Right-click Unturned in your Steam Library
- Select Properties...
- Hover over Manage
- Click Browse local files
- Open the Logs folder
The most recent or currently running file is "Client.log", and "Client_Prev.log" is the log from before the game was restarted.
If you are looking for server log files please refer to this article: Where are the dedicated server log files?