The ESXi host log files are very similar to vCSA logs and can be found in the /var/log/ directory of the host:
[root@esxi-prod-1:/var/log] ls -lahtotal 444drwxr-xr-x 1 root root 512 Feb 16 15:48 .drwxr-xr-x 1 root root 512 Feb 11 20:14 ..-rw-rw-rw- 1 root root 82 Feb 16 15:48 .vmsyslogd.err-rw-r--r-- 1 root root 10.0K Feb 16 15:48 .vmsyslogd.err.1drwxr-xr-x 1 root root 512 Feb 11 20:12 EMUlrwxrwxrwx 1 root root 21 Feb 16 15:48 Xorg.log -> /scratch/log/Xorg.loglrwxrwxrwx 1 root root 21 Feb 16 15:48 auth.log -> /scratch/log/auth.log-rw-rw-rw- 1 root root 56.7K Feb 11 20:14 boot.gzlrwxrwxrwx 1 root root 22 Feb 16 15:48 clomd.log -> /scratch/log/clomd.loglrwxrwxrwx 1 root root 29 Feb 16 15:48 clusterAgent.log -> /scratch/log/clusterAgent.log ...