Question: Problem 2.7 In the paper The Significant Digit Phenomenon, American Mathematical Monthly, Vol. 102, No. 4, April 1995, the author proposes the following probability distribution

Problem 2.7 In the paper The Significant Digit Phenomenon, American Mathematical Monthly, Vol. 102, No. 4, April 1995, the author proposes the following probability distribution for the first significant digit: P(sd) = log10 1 + 1 d , d = 1, 2,..., 9. Here, sd is the event that the first significant digit is the integer

d. Show, using only properties of the log function, that 1≤d≤9 log10 1 + 1 d = 1. Hint: It suffices to show that 1≤d≤9 1 + 1 d = 10.

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