Really weird issue with kali installed on a 100GB HDD partition

First of all, sorry, I'm not a native English speaker.
I will first explain what happened.
I was using kali linux 4.4.0 on a partition of 100GB, it worked perfect, I installed nvidia drivers and i was using cudaHashcat for some days, but today, I saw a message that i have only 500MB left on the hard drive, i had like 30GB used this morning so i tought it was an error, I opened the disk usage analyzer it has installed and i noticed, that /var/log was using a lot of space, but the folders inside were only 4KiB and the bigger 15MiB, so i hoped it was only an error, so I reboot the system and couldn't login, the login screen didn't appear, it only showed a login console blinking, and i couldn't type anything, so i plugged my "panic" usb stick with kali on it and i took a picture of the /var/log usage.
Could someone help me fixing this issue, please?
Attachment 1458

I got the solution HERE for whoever has the same problem.