The log files on the Raspberry Pi can sometimes be a little tricky to locate. Different processes log data to different files on the Raspberry Pi so there are a number of places that you can look to find the log files that you need.
System log files
Here is a list of the most important system log files:
/var/log/messages - Contains all kernel- and driver-related information.
/var/log/auth.log – Contains system authorization information.
/var/log/boot.log – Contains information that is logged when the system boots up.
/var/log/daemon.log – Contains information logged by the various background daemons.
/var/log/dpkg.log – Contains information that is logged when a package is either installed or removed using dpkg.
/var/log/maillog - Contains the mail server log information.
/var/log/mail.log - Contains the mail server log information.
/var/log/cups – Contains all printer and printing related log messages on the Raspberry Pi.
Application log files
If you're looking for log files for a webserver (such as Lighttpd, Apache or Nginx) on the Raspberry Pi, then they will be located wherever you define in the configuration files for the webserver. (Usually in the httpd.conf file). Similarly, for any other process or daemon (such as an FTP server or database server, the location of these log files will be determined by the configuration files.
Lastly, if you miss something that is happening during the boot process, you can type in '''dmesg and it will print out a log of the events that happened during the boot process.