If your logger class exposes its current message, then you need to compare that:
bool bMessageexists = logMessages.Contains(logger=>logger.Message == sMessage);
If not, you will need to override Logger.Equals, to compare the messages in both objects.
class Logger {
string sMessage;
public override bool Equals(object obj) {
if (obj is Logger)
return sMessage == ((Logger)obj).sMessage;
return false;
}
}