In computing $2^{10}\approx10^3$ so what is $10$ approximately equal to?

Question

In computer science $$10^3=1000\approx2^{10}=1024$$ What would be the estimate for $10$? Would it be $$2^3=8$$ or $$2^4=16$$

Answer 1

As you've noted, $2^n$ isn't all that close to $10$ for integers $n$. You could write $10\approx 2^{10/3}$: in fact $2^x=10$ with $x\approx 3.322\approx\frac{33}{10}+\frac{2}{90}=\frac{299}{90}$.