Jim posted a walkthrough on how to get the log files for your Cloud Service when it's running on Windows Azure, you can piece together the info from the SDK docs and looking at the portal, but this walkthrough will streamline the experience for you.

On Windows Azure, you can output trace messages when your Roles are running "in the cloud".  You write the messages by calling the RoleManager.WriteToLog() API in Microsoft.ServiceHosting.ServiceRuntime. 

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