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There are some stars in the NASA Exoplanet Archive that I am interested in but I am confused by the physical meaning of the terms.

For example, there's a star BD+15 2940 with a log10 of Solar Luminosity of 2.01 +/-0.75 where the variation is also a log.

So is the linear equivalents 18.2 to 575.44 with most likely value 102.33?

I went to the citing paper Nowak et al. 2013and they quote it as log L*/LSun 2.01 +/- 0.75 as per the NASA archive.

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You're completely right, except that the authors, as far as I can see, don't specify whether the central value (i.e. $\log L = 2.01$, or $L = 102$) is the most likely value (i.e. the mode), or the average, or the median. My guess is it's the average, but especially for logarithmically distributed values, my opinion is that the median would makes more sense to quote, since in that case you'll get the same result whether you take the median of $L$ or of $\log L$.

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