2¹⁰ = 1024
2²⁰ = 1048576
Note that raising 2 to each of the first two multiples of 10 results in a number whose first digit is 1.

Find the smallest multiple of 10 where 2 raising to that power results in a number that does not begin with 1.

(In reply to worked out by Charlie)

....., so that 1024^29 will still begin with 1...

The word still is misleading, there were numerous 2^k beginning with 1, where k<300,   The 30 is the 1st number  m,  for which 2^(10m)begins with the digit 1.

Just check for k=291 thru 299 or even 11 thru 19.

Edited on April 15, 2015, 10:41 am

Posted by Ady TZIDON on 2015-04-15 09:35:29