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Display the contents of a log file as it is updated

I have external programs such as ffmpeg and gstreamer running in the background and writing to a log file. I want to display the contents of this log with my Flask application, so that the user can watch the log update, like tail -f job.log would do in the terminal.

I tried to use <object data="/out.log" type="text/plain"> to point at the log file, but that failed to show the data, or the browser told me I needed a plugin.

How can I embed and update the log file in an HTML page?