How many bits are needed to represent each integer?
The only one I don't get is this one:
3^1000
How are you even supposed to figure that one up?
The answer in the back of the book is 1585 but I don't know how to get it myself.
Which ones did you get?
$\displaystyle 3^{1000}\;= \;2^{x}$
Solve for 'x'.
It is not a difficult logarithm problem, but I'm not quite sure why 1 was not added to the result.
$\displaystyle 4 = 2^{x} \implies x = 2$, but $\displaystyle 4_{10}\;=\;100_{2}$, and that's clearly not 2 binary digits.