LMDE File system using all 20gb partition (SOLVED)

[Fornhamfred]

I have installed LMDE on a friends computer allocating 20gb for the file system and 10gb for Home. After only a week a message came up today stating that there was no room left on the file system partition and checking have found it to be true. I have the same installation and my file system only uses 3.5gb. I have had to enlarge the partition to 40gb to get the system booting. Can anyone suggest what may be causing the very large usage please?

[asermax]

Try running the Disk Usage Analyser utility (baobab) over the root partition to have an idea of which file/folder is the one using up all the disk space.

[Fornhamfred]

Thanks for the suggestion. The problem lies in the log files. kern.log and syslog both show file sizes of 8.6gb. Is it possible to delete these files?
I have opened kern.log in gedit and it shows no output.
Any help would be appreciated.

Edit: After googling this problem I found I was unable to delete the files but by running this script I have emptied the files:

sudo rm /var/log/messages.0
tail /var/log/messages | sudo tee /var/log/messages.new
tail /var/log/syslog | sudo tee /var/log/syslog.new
tail /var/log/kern.log | sudo tee /var/log/kern.log.new
sudo mv /var/log/messages.new /var/log/messages
sudo mv /var/log/syslog.new /var/log/syslog
sudo mv /var/log/kern.log.new /var/log/kern.log

Partition usage after running script. 4.8gb