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

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%.

Explanation:

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Answer 2

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

Explanation: