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This article has not been completed yet. However, it may already contain helpful Information and therefore it has been published at this stage.
# Log in to the ESXi Shell as root.
ssh root@<ip / hostname>
# Enter your password
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# Retrieving syslog configuration
esxcli system syslog config get
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# Remote Host Configuration
esxcli system syslog config set --loghost='<tcp/udp>://<IP>:<Port>'
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# Syslog - Setting Refresh
esxcli system syslog reload
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# Check Syslog - Firewall-Settings
esxcli network firewall ruleset list
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# Allowing syslog traffic through the ESXI firewall
esxcli network firewall ruleset set --ruleset-id=syslog --enabled=true
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# Firewall - Setting Refresh
esxcli network firewall refresh
# The new settings get active without a reboot or service restart.
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# Check Syslog - Firewall-Settings
esxcli network firewall ruleset list | grep "syslog"
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References:
How to forward ESXi syslog