AnswersFL-1200330-Algebra 2 CRProperties of Logarithms

Properties of Logarithms Answers

14 verified answers4 views
1
Free Preview

Given and , what is ?

Question illustration
A
1.404
B
1.739
C
2.773
D
2.988
2
Free Preview

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
3

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
4

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
5

What is written as a single logarithm?

Question illustration
A
log Subscript 3 Baseline 2 z
Option A
B
log Subscript 3 Baseline 2 z squared
Option B
C
log Subscript 3 Baseline StartFraction z squared Over 4 EndFraction
Option C
D
log Subscript 3 Baseline StartStartFraction 64 z squared Over StartFraction 81 OverOver 49 EndEndFraction
Option D
6

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?

Question illustration
A
The error is in step 3. The reason should be the quotient property of exponents.
B
The error is in step 3. You cannot use a property of logarithms to prove that same property.
C
The error is in step 2. The reason should be the quotient property of exponents.
D
The error is in step 5. The student did not convert from exponential to logarithmic form correctly when solving for x and y.
7

Given and , what is ?

Question illustration
A
1.118
B
1.893
C
2.402
D
3.542
8

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

A
log StartFraction p + 2 Over 18 EndFraction
Option A
B
log StartFraction 18 Over p + 2 EndFraction
Option B
C
log StartFraction 20 Over p EndFraction
Option C
D
log left-bracket 18 times (p + 2) right-bracket
Option D
9

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
10

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
11

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
mc029-1.jpg
Option A
B
mc029-2.jpg
Option B
C
mc029-3.jpg
Option C
D
mc029-4.jpg
Option D
12

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
13

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
14

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?

Question illustration
A
–58 Db
B
–50 Db
C
9 Db
D
50 Db
15

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
16

Given and , what is ?

Question illustration
A
1.404
B
1.739
C
2.773
D
2.988
17

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
18

What is written as a single logarithm?

Question illustration
A
log Subscript 3 Baseline 2 z
Option A
B
log Subscript 3 Baseline 2 z squared
Option B
C
log Subscript 3 Baseline StartFraction z squared Over 4 EndFraction
Option C
D
log Subscript 3 Baseline StartStartFraction 64 z squared Over StartFraction 81 OverOver 49 EndEndFraction
Option D
19

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.
20

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

A
log3 – log(x + 4)
B
log12 + logx
C
log3 + log(x + 4)
D
StartFraction log 3 Over log (x + 4) EndFraction
Option D

Did you find these answers helpful?

More from this Course

Quiz
21 verified answers

Properties of Logarithms

Quiz
10 verified answers

Properties of Logarithms

Quiz
10 verified answers

Properties of Logarithms