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i would like to understand how authours calculate this formula ( log(2^-(x-y)) in the graph below? is it a 10 or 2 based logarithm? Thank you

enter image description here

Mittens
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Mo Kh
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    $\log(2^{-(x-y)})=-(x-y)\log(2)$. As for what base the logarithm is, it depends on context and field of study. Often times you will see $\log$ be the base 10 logarithm while $\ln$ will be the natural log, however there are those authors who use $\log$ as the natural log. In the fields of combinatorics and computer science you may even see it as base $2$. All choices of bases for logarithms cause the results to be just different by a scalar multiple from one another, so many applications it doesn't much matter in the end which it was. – JMoravitz Apr 22 '21 at 02:39

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As a biology-adjacent paper, I would guess that this is base $10$. But as JMoravitz says, it may not matter. In particular, if the only purpose here is to suggest a negative linear correlation, then the graph does that regardless of the base, since if

$$ (x\text{-axis}) \propto -\log_b(2^{\Delta C}) = -\log_b(2)\cdot\Delta C$$

we can absorb any change-of-base factor $\log_b(2)$ into the constant of proportionality.

Eric Nathan Stucky
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