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.

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- Oct 1st 2008, 11:24 AMMadBinary
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. - Oct 1st 2008, 12:28 PMTKHunny
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.