I have a very similar script that lets me write notes to a file with today's filestamp. I use it to keep track of what I've done on which days.
#!/bin/sh
mkdir ~/.worklog || true
if [ -z "$1" ]; then
cat ~/.worklog/$(date +%w).md
else
echo "$(date): $*" >> ~/.worklog/$(date +%w).md
fi
That gives a file per-week which can either have contents appended to it, or viewed. Usage is the obvious: $ worklog "I did some stuff"
$ worklog [shows the output] $ logger hello
$ logger <<EOF
> this is a multiline
> logging message
> EOF
$ sudo journalctl -t vacri
-- Logs begin at Fri 2017-09-29 10:40:49 AEST, end at Mon 2017-10-02 23:44:13 AEDT
Oct 02 23:40:24 myhost vacri[12320]: hello
Oct 02 23:48:48 myhost vacri[12460]: this is a multiline
Oct 02 23:48:48 myhost vacri[12460]: logging message
syslog is good for some use-cases (eg centralisation), and not so good for others. I imagine most people would prefer your directory-of-easily-findable-history.