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 West Side Story (Posted on 2004-02-15)
Does 9 appear as the leftmost digit in the decimal representation of any power of 2?

Does 7 appear as the leftmost digit in the decimal representation of any power of 37?

Is it possible to find a power of any counting number that has a given digit as its leftmost digit?

Also, is it possible to find a power of any counting number that begins with a given series of digits (e.g., is there a power of 24 that begins with 937)?

Prove that this is possible, or give a counter-example.

Bonus: What percentage of the powers of 2 have 1 as their leftmost digit?

Note: In finding the powers of "any counting number," exclude powers of ten, whose leftmost digit is always 1.

 No Solution Yet Submitted by DJ Rating: 3.2500 (8 votes)

 Subject Author Date Slide Rule logic (spoiler) Steve Herman 2012-03-04 11:22:42 re: Initial numbers Federico Kereki 2004-02-16 09:53:45 re: Initial numbers SilverKnight 2004-02-16 09:14:05 Initial numbers e.g. 2004-02-16 08:07:16 re(2): Solution Charlie 2004-02-15 15:18:08 re: Solution Penny 2004-02-15 13:01:34 Solution Charlie 2004-02-15 10:34:43

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