Log footage (S-Log, C-Log, N-Log, V-Log, D-Log, Log-C) is recorded flat and desaturated to hold more dynamic range. Before you grade, you convert it to the standard Rec.709 display space. There are two reliable ways to do it in DaVinci Resolve, and both work in the free version.
Add a node, then apply the Color Space Transform ResolveFX to it. Set Input Color Space and Input Gamma to match your camera (for example Sony S-Gamut3.Cine / S-Log3), and set Output Color Space to Rec.709 and Output Gamma to Gamma 2.4. This is a mathematical conversion, so it is precise and easy to tweak.
Drop your camera's official conversion LUT onto a node instead. It is a one-click "baked" version of the same idea. Grab the correct one from the official camera log LUT library and see how to install a LUT. LUTs are convenient but less flexible than a Color Space Transform.
Whichever method you use, keep the conversion on a dedicated node before your grade. That way you can balance the shot before it and build the look after it, and you can disable the conversion to check the raw log at any time.
For mixed cameras, switch Project Settings → Color Management to DaVinci YRGB Color Managed and set the timeline to Rec.709. Resolve then converts every clip automatically. See color management settings explained.
Color Space Transform is generally cleaner and more flexible because it is a precise math conversion you can adjust. Official LUTs are faster and fine for most work, but they bake in a fixed tone curve.
Gamma 2.4 is standard for video viewed on a calibrated Rec.709 monitor. If your footage looks too dark on typical web and phone screens, some people use Gamma 2.2 instead.
That usually means the input color space or gamma does not match how the footage was shot. Double-check your camera's exact log profile and set the input to match it.