This is a very good question, and detailed enough about the formation of our solar system (which is not my field of astrophysics) that I went and bothered one of my planetary science friends, Alex Parker, to see if this is a coincidence or not, and he immediately recognized this as the Titius-Bode relation.
The Titius-Bode relation is an empirical statement (meaning only that there was an observation that two properties appeared to be correlated with each other) which found that the planets appeared to have a very regular pattern in how far apart they are, as you’ve noticed by taking the log of each of their distances.
However, unless an observed relationship can be explained somehow using physics, it’s difficult to assign any meaning to that relationship. In the case of the Titius-Bode rule, for many years it was accepted as the way that solar systems formed without a physical explanation behind that rule. But it was very convincing, since it predicted the locations of all of the known planets at that time (Mercury, Venus, Earth, Mars, Jupiter, and Saturn). Even Ceres, which is now classified as a dwarf planet, but at the time was considered a planet, seemed to work with it.
However, it’s now largely viewed by the planetary science community as a simple coincidence. Ceres is now known to be one of the larger bodies among the asteroid belt, which is full of a number of smaller (but similar sized) objects, and the predictions failed to explain Neptune’s orbit. There have been a few attempts to “fix” the Titius-Bode relation so that it would work for all the planets, but the evidence for any kind of physical mechanism that would force this relation to be true is so poor that the planetary science journal Icarus does not accept these papers as scientific works.
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