For a randomly chosen real number x on the interval (0,10) find the exact probability of each:
(1) That x and 2^{x} have the same first digit
(2) That x and x^{2} have the same first digit
(3) That x^{2} and 2^{x} have the same first digit.
(4) That x, x^{2} and 2^{x} all have the same first digit.
First digit refers to the first nonzero digit of the number written in decimal form.
(In reply to
An attempt as (3), but it looks wrong according to simulation by Charlie)
I really would like someone to see if I made a logic mistake or some algebraic error, as the simulation result seems too out of line with the analytic calculation for part (3).

Posted by Charlie
on 20110330 09:57:59 