Log files can be of assistance in diagnosing network faults, hardware faults, host faults, VM faults, Guest OS faults, and application faults.
You can see ESX logs:
The vmkernel logs (which log everything related to the kernel/core of the ESX) are located at /var/log/vmkernel.
The vmkwarning logs (which log warnings from the vmkernel) are located at /var/log/vmkwarning.
The vmksummary logs (which provide a summary of system activities such as uptime, downtime, reasons for downtime) are located at /var/log/vmksummary.
The hostd log (which is the log of the ESX management service of the ESX) are located at/var/log/vmware/hostd.log.
The messages log (which log activity on the Service Console operating system) is located at /var/log/messages.
The VirtualCenter Agent log is located at /var/log/vmware/vmware/vpx/vpxa.log.
The Automatic Availability Manager (AAM) logs are located at /var/log/vmware/aam/vmware_<hostname>-xxx.log.
The SW iSCSI logs are located at /var/log/vmkiscsid.log.
The System boot log is located at /var/log/boot-logs/sysboot.log.
You can see ESXi logs:
The VMkernel, vmkwarning, and hostd logs are located at /var/log/messages.
The Host Management service (hostd = Host daemon) log is located at /var/log/vmware/hostd.log\.
The VirtualCenter Agent log is located at /var/log/vmware/vmware/vpx/vpxa.log.
The System boot log is located at /var/log/sysboot.log.
The Automatic Availability Manager (AAM) logs are located at /var/log/vmware/aam/vmware_<hostname>-xxx.log.