# Degrees of Separation to Find Population

Algebra Level 3

It has been calculated that any two random Facebook users are connected by about 4.74 friends, on average (as of 2012). It is quite intimate. On a more inclusive scale, that is, every person on earth, is theoretically connected by approximately 6.6 friends ... "Six Degrees of Separation".

But our goal today has not to do with calculating the degrees of separation, but rather the population of a small boarding school based on such information. In this school, every student knows every other byway of $$2.3$$ friends (giving the word "friend" a loose definition). The average student has $$10$$ friends. What we need to know is the population of the student body.

Expressed in a formula, it looks like this: $\frac { \ln { x } }{ \ln { 10 } } =2.3$

Find the population and round to the nearest whole number. We don't want a fraction of a person.

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