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I want to approximate annual population growth using logarithms; that is, log(population at year 2) - log(population at year 1). Is it okay to use population in thousands, or in millions in these approximations? For example, Maddison Project and PWT provide the population data in thousands and millions.

Ornithogalum
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    By "in millions", do you mean expressed in millions (eg 24.723 M), or rounded to the nearest million (eg 25 M)? – Adam Bailey Jun 10 '22 at 10:41
  • Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Giskard Jun 11 '22 at 06:27

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We have that: $$ \ln(\text{pop in year 2}) - \ln(\text{pop in year 1}) = \ln\left(\frac{\text{pop in year 2}}{\text{pop in year 1}}\right) $$ So if both are measured in millions or in thousands, the resulting number will be the same. In other words, if you take log differences, the scale of measurement does not matter.

tdm
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