the date you installed system

There is no specific log for the date you installed system. But two way to know it from other log. The one is find out the system installer log record what happened when the system be installed. in Debian, sudo head /var/log/installer/syslog could show the date. The second is find out the time the root partition be created. Suppose root partition is /dev/hda1, sudo tune2fs -l /dev/hda1 | grep create could show the date.