Add syslogd as service on Alpine on Docker container

I have a program which needs syslog to run to correctly work. I am working in an Alpine container with version 3.16.0. As I'm getting multiple errors from the program (weewx), I understood that syslog is not running in the container, so I researched how I should run it, with little success. After installing openrc (apk add --no-cache openrc) I tried to add it as a service as it is suggested on the Alpine wiki , however after running rc-update add syslogd boot I got this error:

-update: service `syslogd' does not exist

I don't have a lot of experience with services, so I decided to ask. What should be the right approach to have syslogd run as a daemon when the container is launched? Right now to get it to run I launch it manually, however it would be great to have it run automatically. Thanks!