# Math Help - Binary

1. ## Binary

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.

2. Which ones did you get?

$3^{1000}\;= \;2^{x}$

Solve for 'x'.

It is not a difficult logarithm problem, but I'm not quite sure why 1 was not added to the result.

$4 = 2^{x} \implies x = 2$, but $4_{10}\;=\;100_{2}$, and that's clearly not 2 binary digits.