I am looking at buying a Canon Rebel T6 to record video, but would like to have better audio than the built in microphone. Is there any way, with an adapter or otherwise, that I can use this camera to record video with externally supplied audio?
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Bad news first-
Unfortunately, you are stuck with the in-camera mic with the T6. The T6i has a microphone jack for mounting an external microphone. If you want to mount an external mic to a Canon Rebel T6 body and record that audio stream to the same SD card, that's really your only option.
Can you elaborate a little on what your uses for the video are and what your workflow is?
I have shot on a T6 and T6i extensively and I eventually determined the workflow that was best for me was to use a Zoom H4N as my primary sound recorder (placed somewhere out of sight in the shot) and synced the audio streams together in Adobe Premiere during post production.