You can try this:
heroku logs -n number_of_lines --app application_name >> file_name
>>
operator will appends the command output to the end of a file : file_name
however, heroku keeps the last 1,500 lines of consolidated logs. If you’d like to persist more than 1,500 lines for long-term storage, search, alerting, filtering and other processing, you can use logging Add-on Providers.
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