Log yourself as root with: sudo -s.

# to see the list
find /var/log -maxdepth 1 -type f -name '*.log'

# to purge files to zero byte
find /var/log -maxdepth 1 -type f -name '*.log' -exec sh -c '> {}' \;

You can use find with size flag -size +32M to find files larger than 32MegaBytes

It's safe to assume to delete .gz files in that directory.

Then do

find /var/log -maxdepth 1 -type f -name '*.gz' | xargs rm

It’s possible if you see
rm: missing operand then means:

rm didn't receive arguments since find could not find .gz files.