Apple - How do I find the log for the shutdown process?

Instead of looking at logs, I would start by booting in verbose mode. (It will also shut down in verbose mode.) Just hold Command ⌘ + V at boot.

Check the console for the time of shutdown enter image description here

In the terminal, go to

     /var/log

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Find launchd-shutdown.log that was last modified by your system at the time of shutdown and perform a more on it

     more launchd-shutdown.log

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