Assumming the URL (when accessing via localhost:8080) was http://localhost:8080/appname/Log, the matching URL (when accessing via your domain) should be http://domain/Log (no appname in URL). Is that what you've tried?
BTW, I'm not sure this will work anyway. If you're using a localhost URL to open the app your browser, and the app, from the client-side, tries to access a service on another domain, then this is usually blocked by browser security. Why don't you open the app using the domain URL?
For best results, use the Firefox browser..