Where is Xserver log file located?

Where most of log files located: /var/log/

Log filename: Xorg.0.log Xorg.1.log etc...

Update:

You can check out the log files:

Click on

System menu > Choose Administration > System Log

or

Applications > System Tool > Log File Viewer

/var/log/ as mentioned, or ~/.local/share/xorg/:

If a problem occurs, view the log stored in either /var/log/ or, for the rootless X default since v1.16, in ~/.local/share/xorg/.

- ArchWiki

Note that ~ is a home directory of an user who starts xserver. This user could be gdm3 for example and in such case you will find logs at /var/lib/gdm3/.local/share/xorg.