The probability that the number 1 is the leading digit is \(0.301\).
Given information:
Benford’s law states that the probability that a number in a set has a given leading digit \(d\), is \(P(d) =\log(d+1)-\log(d)\)
As mentioned in question,
Probability of a number in a set is given by \(P(d) =\log(d+1)-\log(d)\).
The division property of logarithm should be use to make it as a single logarithm \(P(d)=\log(\frac{d+1}{d})\;\;\;\{\log(a)-\log(b)=\log\frac{a}{b}\}\).
So, the probability that the number 1 is the leading digit is,
\(P(1) = \log ( ( 1+1)/ 1)\\P(1) = \log ( 2)\\P(1) = 0.301\\\)
Hence, The probability that the number \(1\) is the leading digit is \(0.301\).
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