Shooting in LOG can save your butt if you have some highly reflective areas in the scene. But grading from LOG can be a challenge, to me at least. I use DaVinci Resolve for all my post processing. It takes a little time and some reading to figure out how to proceed. I'm not anywhere near understanding all of it but I've gotten to the point where I can take footage shot from different cameras, some in LOG and others not, and get them looking alike, at leas to the point where a viewer isn't aware of the differences in how each clipin the final sequence was shot.
My insight is to look at the clips, determine what the biggest difference is between them (like contrast), and adjust that first. Ideally, one of the clips in that first comparison should be a really important scene that also looks pretty good to start. That can serrve as the reference to which the other clips are matched. If that clip was shot in LOG, it'll need some adjusting (like contrast and saturation) right off the bat before you can use it as a reference. Get it looking good, and then compare other clips to it for color balance (tone, sasturation, contrast, etc.).
I often start with contrast. The various scopes (like the waveform) in DaVinci can help to get the brights equally bright and the darks equally dark across clips. Then, look at what the next biggest difference is (like overall saturation), and adjust that. At some point, the clips will look close but you'll still se a noticable shift when you scroll from one to the next. That's usually when some finer tuning is called for.
At that stage, I look specifically at highlight areas in both clips and see how (or if) they differ. Are the highlights pinker in one than the other, for example. Do the shadows on one have a bluish tint the othe other clip lacks? Are there still differences in the midtones? These finer adjustments to specific parts of the tone spectrum can be tricky. But saving them for near the end of the process helps. There's likely to be some back-and-forth as every change will have some unintended consequences. Dark, mid, and bright areas aren't mutually exclusive. They overlap. It can take some time to get things balances across clips. Before a change, try to keep track of where the image was (make note of the relevant values) so that you can undo it if needed. Similarly, color contrast (i.e., saturation) and luminance contrast aren't fully independent. Making really small changes is usually best. A few successive big changes can leve you with a mess and you may have some difficult undoing the damage. Proceed in small increments.
I'm getting better at this with practice. It's still definitely a challenge but I enjoy the process. It's taught me both the value of shooting in LOG and of using an ND filter on bright days, among other things. Hope some of these suggestions help others.