Math Is Fun Forum

juantheron

Member

Registered: 2011-10-19

Posts: 312

first digit

Select a non-negative integer n at random. What is the probability that the first digit of 2^n  is  a ``one'' (in base 10 notation)?

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: first digit

Hi juantheron,

Using a computer, the probability appears to be

I tried till n = 30000, which showed that there are 9031 numbers beginning with '1'.

Here's the solution: http://www.mathnerds.com/best/digit/index.aspx

Last edited by gAr (2011-12-23 05:57:09)

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bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: first digit

Hi juantheron and gAr;

Using Bensfords law or the logarithmic law as Knuth calls it the probability is log(2) to the base 10.

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