Properties of Logarithms

Question 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).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.

Revolt · Accepted Answer

To rewrite the expression, use the quotient property of logarithms, which states that log(a) - log(b) = log(a/b). The expression becomes P(d) = log((d + 1) / d). To find the probability that 1 is the leading digit, substitute d = 1 into the expression: P(1) = log((1 + 1) / 1) = log(2). Since log(2) is approximately 0.301, the probability that the first digit is 1 is approximately 30.1% or 0.30.

Question 2

Question 2

Revolt · Accepted Answer

: A; : D; : B

Question 3

= AB✔ CD

Revolt · Accepted Answer

C: ✔ C

Question 4

substitutioncommutative property

Revolt · Accepted Answer

C:

Question 5

Which of the following did you include in your solution?

Revolt · Accepted Answer

PENDING

Question 6

= ✔ ABCD

Revolt · Accepted Answer

A: ✔ A

Question 7

= ABC✔ D

Revolt · Accepted Answer

D: ✔ D

Question 8

= A✔ BCD

Revolt · Accepted Answer

B: ✔ B

Properties of Logarithms Answers

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