Per capita means per head or per person.
now, if a country has a small GDP hmmm say for the sake of example, $1000, and it has 1000 residents, then the per capita is $1000/1000 or a buck each.
now, $1000 is a really tiny GDP, but, if the population is say hmm 20 folks only, then the per capita amount is $1000/20, or $50 per person, now, that's a large "per capita" figure, more so than $1 per person, even though the GDP never changed, it was all along $1000.
so, if the population is comparitively small, the per capita is large, I think a good example of that is Switzerland.
sidenote:
bear in mind that per capita figures are very misleading, since you could have a tiny portion of the population making huge amounts and others making little, like in the US, and the per capita is very inaccurate to reflect the economy wealth distribution.
Given:
Consider the equation is:
To prove:
by using the properties of logarithms.
Solution:
We have,
Taking left hand side (LHS), we get
![\left[\because \log_ab=\dfrac{\log_x a}{\log_x b}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbecause%20%5Clog_ab%3D%5Cdfrac%7B%5Clog_x%20a%7D%7B%5Clog_x%20b%7D%5Cright%5D)
![[\because \log x^n=n\log x]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Clog%20x%5En%3Dn%5Clog%20x%5D)
Hence proved.
