Yes, you probably should. Shooting in RAW and LOG are different things, and each has an effect, primarily on your film look in post. With RAW, what you are doing is preserving the uncompressed camera data. This gives the post deck more data resolution (not pixel resolution) to work with, and results in things like smoother gradients or hue transformations.
LOG basically functions as a way to focus or powerband contrast resolution where it's most useful, at least in terms of getting a more classic film look.
When you see footage shot without these workflows, all that is is the device or program automatically converting the footage to a preset color space for easier storage and playback. Well, it's a bit more complicated, but basically, shooting uncompressed and log footage puts full control of that process back in your hands, and that can be valuable in practical ways in many different scenarios.
Example Given: You are shooting a horror movie in dim light, to sell a feeling of unease. Your iphone auto colors it to be bright and clear, ruining the effect you were going for. Solution: shoot raw and use manual controls in post to enhance contrast without brightening the entire picture.