AnswersAA - F26 Advanced AlgebraProperties of Logarithms

Properties of Logarithms Answers

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1
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Which of the following is equivalent to ?

Question illustration
A
log one-ninth minus log k
Option A
B
log 1 minus log StartFraction 9 Over k EndFraction
Option B
C
log one-ninth minus k
Option C
D
log one-ninth + log k
Option D
2
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Which expression is equivalent to ?

Question illustration
A
4 log Subscript w Baseline StartFraction x squared Over 1296 EndFraction minus one-third log Subscript w Baseline (2 x + 8)
Option A
B
4 log Subscript w Baseline (x squared minus 6) minus one-third log Subscript w Baseline (x squared + 8)
Option B
C
4 log Subscript w Baseline (X squared minus 6) minus one-third log Subscript w Baseline (x squared + 8)
Option C
D
4 (log Subscript w Baseline x squared minus one-third log Subscript w Baseline (x squared + 8) minus 6)
Option D
3

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?

Question illustration
A
Brandon’s sound intensity is the level of Ahmad’s mower.
Option A
B
Brandon’s sound intensity is the level of Ahmad’s mower.
Option B
C
Brandon’s sound intensity is 20 times the level of Ahmad’s mower.
D
Brandon’s sound intensity is 80 times the level of Ahmad’s mower.
4

Which expression is equivalent to ?

Question illustration
A
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
Option A
B
log Subscript 8 Baseline 4 + log Subscript 8 Baseline a + (log Subscript 8 Baseline (b minus 4) minus 4 log Subscript 8 Baseline c)
Option B
C
log Subscript 8 Baseline 4 a + log Subscript 8 Baseline b minus 4 minus 4 log Subscript 8 Baseline c minus 4
Option C
D
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
Option D
5

What is written as a single log?

Question illustration
A
log Subscript 5 Baseline 21
Option A
B
log Subscript 5 Baseline 26
Option B
C
log Subscript 5 Baseline 30
Option C
D
log Subscript 5 Baseline 56
Option D
6

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?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
7

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?

Question illustration
A
mc027-7.jpg
Option A
B
mc027-8.jpg
Option B
C
mc027-9.jpg
Option C
D
mc027-10.jpg
Option D
8

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

Question illustration
A
; power rule of exponents
Option A
B
subtraction property of exponents
Option B
C
multiplication rule of exponents
Option C
D
division property of exponents
Option D
9

Which expression is equivalent to ?

Question illustration
A
log Subscript 3 Baseline c + log Subscript 3 Baseline (9)
Option A
B
log Subscript 3 Baseline (9) + log Subscript 3 Baseline (c)
Option B
C
log Subscript 3 Baseline c minus log Subscript 3 Baseline (9)
Option C
D
log Subscript 3 Baseline (9) minus log Subscript 3 Baseline (c)
Option D
10

What is written as a single logarithm?

Question illustration
A
log Subscript 5 Baseline (25 x Superscript 5 Baseline) RootIndex 3 StartRoot x squared + 6 EndRot
Option A
B
log Subscript 5 Baseline (25 x Superscript 6 Baseline) RootIndex 3 StartRoot x squared + 6 EndRoot
Option B
C
log Subscript 5 Baseline 25 x Superscript 5 Baseline + log Subscript 5 Baseline 2 + log one-third x squared
Option C
D
(log Subscript 5 Baseline 25 + log Subscript 5 Baseline Superscript 6 Baseline) (log Subscript 5 Baseline RootIndex 3 StartRoot x squared + 6 EndRoot)
Option D

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