(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
re: exploration turned up something strange by Charlie)
So much for a trusty calculator.
It turns out I encountered a flaw in the way it finds the intersection of two functions. The firsttwodigits function has discontinuities similar to a greatest integer function. P1 passes through most of these gaps. Whatever variation of Newtons method it uses, sometimes things just go wrong in these cases. Instead of reporting no solution it reported a solution that isnt even very close.
Yesterday, I though I was going to get solutions like 2^13.55075 = 12000.026738460294. I will leave it at this. This could make a nice extension of the problem.

Posted by Jer
on 20110317 13:58:24 