Overview
Use `log`.
Streaming (like tail command)
`log stream`
Find from past log
`log show`
See `man log` for detail.
Example
cron
$ log stream --info --predicate 'process == "cron"'
$ log show --info --predicate 'process == "cron"' --start '2017-05-25'
postfix
$ log stream --info --predicate '(process == "smtp") || (process == "smtpd")'
$ log show --info --predicate '(process == "smtp") || (process == "smtpd")' --start '2017-05-25'
If you doesn't know process name to specify
$ log show --info --start '2017-11-08' | grep 'xxx'
and guess process name.