# Calculating algorithm sizes

I am reviewing BigO notation from this document: http://www.scs.ryerson.ca/~mth110/Handouts/PD/bigO.pdf

This document contains this information and the accompanying table:

In the following table we suppose that a linear algorithm can do a problem up to size 1000 in 1 second. We then use this to calculate how large a problem this algorithm could handle in 1 minute and 1 hour.

I can see where values such as $n^2$ come from, as it is getting the square root of 1000. However, I am at a loss as to how the author calculated $2^n$ and $n log(n)$. Could someone help determine how these values are calculated?

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For $2^n$, you just take the logarithm to the base $2$.
For $n\log n$, you are looking for the largest integer $n$ such that $n\log n$ does not exceed, say, $1000$. You can do that by just trying different values of $n$, zeroing in on the right value; there are more systematic ways, such as Newton's Method --- someone just asked a question here about solving $n\log n\le1,000,000$, maybe you could dig up that question and see what's written there.