Answers College Prep Math B - IC26Properties of Logarithms

Properties of Logarithms Answers

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The proof for the power property of logarithms appears in the table with an expression missing. StepReasonGivenSubstitution Properties of exponentsLogarithm property SubstitutionCommutative property of multiplicationWhich expression is missing from the proof?

Option

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The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as , where and is the least intense sound a human ear can hear. Brandon is trying to take a nap, and he can barely hear his neighbor mowing the lawn. The sound intensity level that Brandon can hear is 10-10. Ahmad, Brandon’s neighbor that lives across the street, is mowing the lawn, and the sound intensity level of the mower is 10-4. How does Brandon’s sound intensity level compare to Ahmad’s mower?

Brandon’s sound intensity is the level of Ahmad’s mower.

Brandon’s sound intensity is 20 times the level of Ahmad’s mower.

Brandon’s sound intensity is 80 times the level of Ahmad’s mower.

Which expression is equivalent to log3(x + 4)?

log3 – log(x + 4)

log12 + logx

log3 + log(x + 4)

StartFraction log 3 Over log (x + 4) EndFraction

Which of the following is equivalent to log9w?

log9 + logw

log9 - logw

w(log9)

9(logw)

Which expression is equivalent to ?

log Subscript c Baseline x squared minus log Subscript c Baseline 5 x minus 1

2 log Subscript c Baseline x minus (log Subscript c Baseline 5 + log Subscript c Baseline x) minus 1

log Subscript c Baseline (x squared minus 1) minus (log Subscript c Baseline 5 + log Subscript c Baseline x)

2 log Subscript c Baseline x minus log Subscript c Baseline 1 minus log Subscript c Baseline 5 + log Subscript c Baseline x

When proving the product, quotient, or power rule of logarithms, various properties of logarithms and exponents must be used. Which property listed below is used in all of these proofs?

Option

What is written as a single log?

log Subscript 5 Baseline 21

log Subscript 5 Baseline 26

log Subscript 5 Baseline 30

log Subscript 5 Baseline 56

Which of the following is equivalent to ?

log one-ninth minus log k

log 1 minus log StartFraction 9 Over k EndFraction

log one-ninth minus k

log one-ninth + log k

What is written as a single logarithm?

log Subscript 5 Baseline (25 x Superscript 5 Baseline) RootIndex 3 StartRoot x squared + 6 EndRot

log Subscript 5 Baseline (25 x Superscript 6 Baseline) RootIndex 3 StartRoot x squared + 6 EndRoot

log Subscript 5 Baseline 25 x Superscript 5 Baseline + log Subscript 5 Baseline 2 + log one-third x squared

(log Subscript 5 Baseline 25 + log Subscript 5 Baseline Superscript 6 Baseline) (log Subscript 5 Baseline RootIndex 3 StartRoot x squared + 6 EndRoot)

Which expression is equivalent to ?

4 log Subscript w Baseline StartFraction x squared Over 1296 EndFraction minus one-third log Subscript w Baseline (2 x + 8)

4 log Subscript w Baseline (x squared minus 6) minus one-third log Subscript w Baseline (x squared + 8)

4 log Subscript w Baseline (X squared minus 6) minus one-third log Subscript w Baseline (x squared + 8)

4 (log Subscript w Baseline x squared minus one-third log Subscript w Baseline (x squared + 8) minus 6)

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Properties of Logarithms Answers

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