Question

Benford’s law states that the probability that a number in a set has a given leading digit, d, is

Answer 1

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)  
The division property of logarithm should be use to make it as a single logarithm  
P(d) = log ( (d + 1)/ d)  
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

Answer 2

The exact right answer fore this question would be...

Use the quotient property to rewrite the expression.

Write the difference of logs as the quotient log((d+1)/d).

Substitute 1 for d to get log(2).

Since log(2) = 0.30, the probability that the number 1 is the leading digit is about 30%.