Okay, I Analyzed your log file with the Analyzer of this Website and you should look out for:
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Multiple video cards detected
If you are having problems and are using a laptop, see
this thread (
https://obsproject.com/forum/threads/laptop-black-screen-when-capturing-read-here-first.5965/) for advice.
If you are using SLI or Crossfire, you may need to disable it for compatibility with OBS.
Excessive bitrate
Your bitrate is very high. For live streaming, your viewers must also be able to download at the bitrate you specified. Setting too high of a bitrate will cause your viewers to experience lag and your stream may also drop frames if the streaming service you use does not support such high bitrates.
Skipped frames detected
The video encoder is unable to encode your frames in realtime, causing skipped frames (the video output will appear frozen). This is often caused by running at too high of a resolution / FPS combination for your CPU. Try lowering your resolution and/or FPS. If you have changed the x264 preset, put it back to default (veryfast).
See
https://obsproject.com/forum/thread...ing-too-long-to-encode-read-this-first.23334/ for more details on how to fix this problem.
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That just about your whole Stream.
Back to your main Problem, try grapping the Elgato with "Video Capture device".
Also you should know there are ongoing problems with Elgato and OBS, read about that in this thread: (
https://obsproject.com/forum/threads/elgato-game-capture-hd60.18679/)