That's neither logarithmic nor what log cameras capture. See the link posted by the sibling comment[1] for the actual curves.
If you see an S-curve, that's usually what you will try to map the captured images too because it allows for increased detail in both shadows and highlights, while allowing a natural dynamic range in the middle areas. Log capturing allows you to have a much higher dynamic range (with a given number of bits), and thus more easily map to the S-curve that you want.
I think that s-curve is the target (i.e. the overall end-to-end system gamma, combining the encoding and decoding transfer functions). If it's linear to reproduce the source, but for various reasons [1] sometimes it's preferable to have a gradual roll-of
