Why does Benford's Law (or Zipf's Law) hold? Both Benford's Law (if you take a list of values, the distribution of the most significant digit is rougly proportional to the logarithm of the digit) and Zipf's Law (given a corpus of natural language utterances, the frequency of any word is roughly inversely proportional to its rank in the frequency table) are not theorems in a mathematical sense, but they work quite good in the real life. 
Does anyone have an idea why this happens?
(see also this question)

Let's take two quantities that we're counting:

*

*Quantity L grows linearly. It starts at 100 and grows by 1 unit per day

*Quantity E grows exponentially. It starts at 100 and grows by 1% per day

If we record these quantities every day for a long time, we'd see that it takes L as much time to go from 1000 -> 2000 as it does to go from 8000 -> 9000 whereas for E, it will take longer to go from 1000 -> 2000 than it would to go from 8000 -> 9000. This remains true for all orders of magnitude. This generalises to all quantities that grow exponentially and thus all processes that grow exponentially will spend longer with their leading digit as 1 than 2 and longer at 2 than 3 and .....
As most processes in nature grow exponentially (size of a settlement, number of trees in a forest, salaries, number of covid cases, ....), we see that the leading number of things we measure will disproportionately be 1
Note: As a previous poster pointed out, this applies to anything growing at a 'rate'. Not just growing exponentially.
