Hi all, any ideas with the following?

Let n be a positive integer:

Show that when n is written in binary notation, then the number k of its digits

satises

k - 1 <= ln(n)/ln(2) < k

where ln is the natural logarithm.

Thanks!

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- May 2nd 2011, 05:02 PMsirellwoodBinary Integer Proof?
Hi all, any ideas with the following?

Let n be a positive integer:

Show that when n is written in binary notation, then the number k of its digits

satises

k - 1 <= ln(n)/ln(2) < k

where ln is the natural logarithm.

Thanks! - May 2nd 2011, 06:19 PMtonio
- May 3rd 2011, 04:22 AMsirellwood
So could I use the same theory for when n is written in decimal notation, then the number L of its digits

satisfies:

L-1 <= ln(n)/ln(10) < L?