(A) For a base ten positive integer P drawn at random between 10 and 99 inclusively, determine the probability that the first two digits (reading left to right) in the base ten
expansion of 2^{P} is equal to P1.
(B) For a base ten positive integer P drawn at random between 10 and 99 inclusively, determine the probability that the first two digits (reading left to right) in the base ten expansion of 6^{P} is equal to P1.
(In reply to
exploration turned up something strange by Jer)
I'm not sure what you are referring to. To begin with I don't know what a nonintegral solution would be, as the first two digits would form an integer and so could be 1 less than some other integer.
Do you mean something like 2^13.55075 = 12000.026738460294, where the integer part of P equals 1 more than the integer formed from the first two digits of 2^P?
Edited on March 16, 2011, 3:42 pm

Posted by Charlie
on 20110316 15:41:49 