No, that's not normal. Perhaps someone can help you to find out what fills the logs. On my system the logs in /var are alltogether 232 MB, but I have set up a config file to limit the space to max 200M because I have a very small drive with only 128 GiB.
I used that guide (but didn't enable
MaxRetentionSec=1w), but I think it is similar to the guide from Aravisian here but uses another config file.