Question: [07] (a) Show that for x N we have l(x) = log(x + 1). (b) Give another code c(x) for the natural numbers x

[07]

(a) Show that for x ∈ N we have l(x) = log(x + 1).

(b) Give another code c(x) for the natural numbers x = 1, 2,... such that l(c(x)) = log x.

Comments. Hint for Item (b): Use the correspondence

(, 1),(0, 2),(1, 3),(00, 4),(01, 5),(10, 6),(11, 7),....

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