x is a randomly chosen hexadecimal real number on the interval (0, (10)₁₆)

Determine the probability of each of the following:

(i) x and 3^x have the same first digit.

(ii) x and x³ have the same first digit.

(iii) x³ and 3^x have the same first digit.

(iv) x, x³ and 3^x have the same first digit.

*** “First digit” denotes the first nonzero digit of the number when expressed in hexadecimal form.