Answers KISD SS-3391B-Algebra II Honors BProperties of Logarithms

Properties of Logarithms Answers

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Given and , what is ?

1.404

1.739

2.773

2.988

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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?

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Which expression is equivalent to ?

log Subscript 8 Baseline 4 + log Subscript 8 Baseline a minus log Subscript 8 Baseline (b minus 4) minus 4 log Subscript 8 Baseline c

log Subscript 8 Baseline 4 + log Subscript 8 Baseline a + (log Subscript 8 Baseline (b minus 4) minus 4 log Subscript 8 Baseline c)

log Subscript 8 Baseline 4 a + log Subscript 8 Baseline b minus 4 minus 4 log Subscript 8 Baseline c minus 4

log Subscript 8 Baseline 4 + log Subscript 8 Baseline a minus log Subscript 8 Baseline (b minus 4) minus log Subscript 8 Baseline 4 c

Which expression is equivalent to ?

log Subscript 3 Baseline c + log Subscript 3 Baseline (9)

log Subscript 3 Baseline (9) + log Subscript 3 Baseline (c)

log Subscript 3 Baseline c minus log Subscript 3 Baseline (9)

log Subscript 3 Baseline (9) minus log Subscript 3 Baseline (c)

Sam is proving the product property of logarithms. StepJustificationGivenSubstitution Which expression and justification completes the third step of her proof?

; power rule of exponents

subtraction property of exponents

multiplication rule of exponents

division property of exponents

Which expression is equivalent to ?

log Subscript 3 Baseline c + log Subscript 3 Baseline (9)

log Subscript 3 Baseline (9) + log Subscript 3 Baseline (c)

log Subscript 3 Baseline c minus log Subscript 3 Baseline (9)

log Subscript 3 Baseline (9) minus log Subscript 3 Baseline (c)

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. What is the approximate loudness of a dinner conversation with a sound intensity of 10–7?

–58 Db

–50 Db

9 Db

50 Db

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 log?

log Subscript 5 Baseline 21

log Subscript 5 Baseline 26

log Subscript 5 Baseline 30

log Subscript 5 Baseline 56

Given and , what is ?

1.404

1.739

2.773

2.988

What is written as a single logarithm?

log Subscript 3 Baseline 2 z

log Subscript 3 Baseline 2 z squared

log Subscript 3 Baseline StartFraction z squared Over 4 EndFraction

log Subscript 3 Baseline StartStartFraction 64 z squared Over StartFraction 81 OverOver 49 EndEndFraction

Which expression is equivalent to ?

log Subscript 8 Baseline 4 + log Subscript 8 Baseline a minus log Subscript 8 Baseline (b minus 4) minus 4 log Subscript 8 Baseline c

log Subscript 8 Baseline 4 + log Subscript 8 Baseline a + (log Subscript 8 Baseline (b minus 4) minus 4 log Subscript 8 Baseline c)

log Subscript 8 Baseline 4 a + log Subscript 8 Baseline b minus 4 minus 4 log Subscript 8 Baseline c minus 4

log Subscript 8 Baseline 4 + log Subscript 8 Baseline a minus log Subscript 8 Baseline (b minus 4) minus log Subscript 8 Baseline 4 c

What is written as a single logarithm?

log Subscript 3 Baseline 2 z

log Subscript 3 Baseline 2 z squared

log Subscript 3 Baseline StartFraction z squared Over 4 EndFraction

log Subscript 3 Baseline StartStartFraction 64 z squared Over StartFraction 81 OverOver 49 EndEndFraction

The table shows a student’s proof of the quotient rule for logarithms.Let M = bx and N = by for some real numbers x and y. StepReason1Given2Substitution3Properties of logarithms4Logarithm property logb(bc) = c5SubstitutionWhat is the error in the proof?

The error is in step 3. The reason should be the quotient property of exponents.

The error is in step 3. You cannot use a property of logarithms to prove that same property.

The error is in step 2. The reason should be the quotient property of exponents.

The error is in step 5. The student did not convert from exponential to logarithmic form correctly when solving for x and y.

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.

Given and , what is ?

1.118

1.893

2.402

3.542

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 expression is equivalent to log18 – log(p + 2)?

log StartFraction p + 2 Over 18 EndFraction

log StartFraction 18 Over p + 2 EndFraction

log StartFraction 20 Over p EndFraction

log left-bracket 18 times (p + 2) right-bracket

Which expression is equivalent to ?

log Subscript 12 Baseline 8 minus log Subscript 12 Baseline one-half + log Subscript 12 Baseline w

log Subscript 12 Baseline one-half minus (log Subscript 12 Baseline 8 + log Subscript 12 Baseline w)

log Subscript 12 Baseline one-half minus log Subscript 12 Baseline 8 + log Subscript 12 Baseline w

log Subscript 12 Baseline one-half divided by log Subscript 12 Baseline 8 + log Subscript 12 Baseline w

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

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)