Question

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).

State which property you would use to rewrite the expression as a single logarithm, and rewrite the logarithm. What is the probability that the number 1 is the leading digit? Explain.

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