Number of possible digits in a binary representation of a number

Hi all,

Suppose that when n is written in decimal notation it has 100 digits. Which
possibilities are there for the number of digits if n is written in binary notation?

Any ideas?

Thanks

Hello, sirellwood!

Quote:

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Suppose that when is written in decimal notation it has 100 digits.
What possibilities are there for the number of digits if is written in binary notation?

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http://latex.codecogs.com/png.latex?...n\:<\:10^{100}

http://latex.codecogs.com/png.latex?...ntained in }n.

. . http://latex.codecogs.com/png.latex?... \:<\:10^{100}

http://latex.codecogs.com/png.latex?...\log(10^{100})

. . . . . . . . . . . . . http://latex.codecogs.com/png.latex?...log 2 \:<\:100

. . . . . . . . . . . . . http://latex.codecogs.com/png.latex?...ac{100}{\log2}

. . . . . . . . . . . . http://latex.codecogs.com/png.latex?...:k \:<\:332.19

. . . . . . . . . . . . . . http://latex.codecogs.com/png.latex?...e\:k\:\le\:332


http://latex.codecogs.com/png.latex?...o 332 digits.}

Quote:

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Originally Posted by Soroban

Hello, sirellwood!


http://latex.codecogs.com/png.latex?...n\:<\:10^{100}

http://latex.codecogs.com/png.latex?...ntained in }n.

. . http://latex.codecogs.com/png.latex?... \:<\:10^{100}

http://latex.codecogs.com/png.latex?...\log(10^{100})

. . . . . . . . . . . . . http://latex.codecogs.com/png.latex?...log 2 \:<\:100

. . . . . . . . . . . . . http://latex.codecogs.com/png.latex?...ac{100}{\log2}

. . . . . . . . . . . . http://latex.codecogs.com/png.latex?...:k \:<\:332.19

. . . . . . . . . . . . . . http://latex.codecogs.com/png.latex?...e\:k\:\le\:332


http://latex.codecogs.com/png.latex?...o 332 digits.}

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This is a very weird question since the OP already posted a question in this same Number Theory asking about this and the answer was there...

Tonio