Write 7z Log During Archive Creation

**Situation:** I get daily backups of my vps onto an external hard disk and I create daily "snapshots" using rsyncd into folders named via the date function. Then I use 7z immediately following the rsync snapshot to create a multi-part archive that I can upload for long-term storage. **Progress** I can do all of the above using the 7z command below:

cd /path/to/external/hd/daily-snapshots/$(date --date="yesterday" +%Y-%m-%d) && cputool --load-limit 5.5 -- 7z a -t7z -m0=lzma2 -mx=9 -aoa -mfb=64 -md=32m -ms=on -mhe -pXXXXX full-$(date --date="yesterday" +%Y-%m-%d).7z * -v5g

**Problem:** How can I write the contents of the archive to a log file?

cd /path/to/external/hd/daily-snapshots/daily-snapshots/$(date --date="yesterday" +%Y-%m-%d) && cputool --load-limit 5.5 -- 7z a -t7z -m0=lzma2 -mx=9 -aoa -mfb=64 -md=32m -ms=on -mhe -pXXXXX full-$(date --date="yesterday" +%Y-%m-%d).7z * -v5g >> /var/log/7z-daily-archive.log

doesn't seem to work... Any thoughts?