My MacBook Air suddenly shut down today, is there an easy way to find the associated log entry?
You can get the previous shutdown cause from the log history.
In macOS Sierra and later with unified logging:
log show --predicate 'eventMessage contains "Previous shutdown cause"' --last 24h
Earlier than macOS Sierra, filer system.log for some recent results:
grep "Previous shutdown cause" /var/log/system.log
Then look up the code on this table I maintain: Previous Shutdown Causes Explained