I'm reading a scientific paper and an equation of the following form appears:

x = y log (z).

I know what y and z are in my own data set. How do I solve for x?

I'm used to logarithms of the form log28, and then I can work out that the base is 2 and hence the answer is 3. How can I go about working out this unfamiliar (to me) form of logarithm? What's the base?

Edit: May as well provide a link to the paper. It's here, and the relevant part is on p264.

  • 3
    $\begingroup$ An unspecified base is 10. so it would be $y log_{10}(z)$ $\endgroup$ Nov 11 '14 at 1:49
  • 4
    $\begingroup$ An unspecified base is also quite often $e$. $\endgroup$ Nov 11 '14 at 1:50
  • $\begingroup$ That would be denoted $ln$ wouldn't it? $\endgroup$ Nov 11 '14 at 1:51
  • 3
    $\begingroup$ In an undergraduate American algebra textbook, yes. In a scientific or mathematical paper, unspecified log can be $e$ or even $2$, even though $\ln$ and $\text{lg}$ are standard elsewhere. $\endgroup$ Nov 11 '14 at 1:52
  • 1
    $\begingroup$ Since it's log-odds, the best guess seems to be $e$. It also looks like there is a parameter scaling the log-odds so that it doesn't matter what base is used. The wiki en.wikipedia.org/wiki/Logit supports multiple possibilities (including 2). stats.gla.ac.uk/glossary/?q=node/272 supports $e$ as standard for log-odds. Also, with $e$ as base, log-odds is the inverse of the logistic function. $\endgroup$ Nov 11 '14 at 3:09

The paper doesn't explicitly mention a base, but later on there's a reference to exponentiation, which indicates that the base is e.


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