AnswersFL-1200330-Algebra 2 CREvaluating Logarithmic Expressions

Properties of Logarithms Answers

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= X ABC✔ D

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= X A✔ BCD

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2.356

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⇒ -1.631

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-1.631

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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.

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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.

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Which of the following did you include in your solution?

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Use the quotient property to rewrite the expression.
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Write the difference of logs as the quotient log((d+1)/d).
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Substitute 1 for d to get log(2).
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Since log(2) = 0.30, the probability that the number 1 is the leading digit is about 30%.
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= AX B✔ CD

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Selection 1:C
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substitutioncommutative property

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commutative property
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43225665,536

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4
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65,536
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= ✔ ABX CD

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