The ESXi host log files are very similar to vCSA logs and can be found in the /var/log directory of the host:
[root@esx1:/var/log] lsXorg.log epd.log iofilter-init.log rabbitmqproxy.log upitd.log vmwareauth.log esxcli-software.log iofiltervpd.log rhttpproxy.log usb.log vobd.logboot.gz esxcli.log ipmi sdrsinjector.log vdpi.log vprobe.logclomd.log esxupdate.log jumpstart-stdout.log shell.log vitd.log vpxa.logcmmdsTimeMachine.log fdm.log kickstart.log smbios.bin vmauthd.log vsanmgmt.logcmmdsTimeMachineDump.log hbrca.log lacp.log storagerm.log vmkdevmgr.log vsansystem.logconfigRP.log hostd-probe.log netcpa.log swapobjd.log vmkernel.log vsanvpd.logddecomd.log hostd.log nfcd.log sysboot.log vmkeventd.log vsfwd.logdfwpktlogs.log hostdCgiServer.log ...
