Properties of Logarithms Answers
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log749 = [___]
2
log798 ≈ [___]
2.356
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log33 = [___]
1
log3 a 3 = [___]
3log3 a
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substitutioncommutative property
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2
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2.356
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1
⇒ -1.631
a
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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.
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.
Which of the following did you include in your solution?
= AX B✔ CD
substitutioncommutative property
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43225665,536
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43225665,536
= ✔ ABX CD
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= X ABC✔ D
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= X A✔ BCD
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