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 x² have the same first digit

(3) That x² and 2^x have the same first digit.

(4) That x, x² and 2^x all have the same first digit.

First digit refers to the first non-zero 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 2011-03-30 09:57:59