There's an awesome open-source SysLog Library for .Net: SyslogNet.
Here's an example where I create a sender, create a message and send it:
_syslogSender = new SyslogUdpSender("localhost",514);
_syslogSender.Send(
new SyslogMessage(
DateTime.Now,
Facility.SecurityOrAuthorizationMessages1,
Severity.Informational,
Environment.MachineName,
"Application Name",
"Message Content"),
new SyslogRfc3164MessageSerializer());