Answers College Prep Math B - IC26Properties of Logarithms

Properties of Logarithms Answers

18 verified answers

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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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 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

What is rewritten using the power property?

log Subscript 15 Baseline 5

log Subscript 15 Baseline 6

2 log Subscript 15 Baseline 3

3 log Subscript 15 Baseline 2

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

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

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

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

Given and , what is ?

1.404

1.739

2.773

2.988

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

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.

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.

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

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)

What is rewritten using the power property?

log Subscript 15 Baseline 5

log Subscript 15 Baseline 6

2 log Subscript 15 Baseline 3

3 log Subscript 15 Baseline 2

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

Given and , what is ?

1.404

1.739

2.773

2.988

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 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)

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