Syslog

A Linux system's syslog resides in the text file /var/log/messages.

Find a reboot

The best way to find a reboot in the syslog is to watch out for the text

syslog-ng starting up

Because usually syslog starts up after a reboot and stays up all the time. You can also watch out for

shutting down for system halt

or

shutting down for system reboot

But it happens frequently that the computer reboots because it has severe errors and these errors prevent it from writing this into /var/log/messages.