AnswersCR - Algebra 2 26-27 - S2Evaluating Logarithmic Expressions

Properties of Logarithms Answers

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1
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What is rewritten using the power property?

Question illustration
A
log Subscript 15 Baseline 5
Option A
B
log Subscript 15 Baseline 6
Option B
C
2 log Subscript 15 Baseline 3
Option C
D
3 log Subscript 15 Baseline 2
Option D
2
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Which expression is equivalent to ?

Question illustration
A
log Subscript 12 Baseline 8 minus log Subscript 12 Baseline one-half + log Subscript 12 Baseline w
Option A
B
log Subscript 12 Baseline one-half minus (log Subscript 12 Baseline 8 + log Subscript 12 Baseline w)
Option B
C
log Subscript 12 Baseline one-half minus log Subscript 12 Baseline 8 + log Subscript 12 Baseline w
Option C
D
log Subscript 12 Baseline one-half divided by log Subscript 12 Baseline 8 + log Subscript 12 Baseline w
Option D
3

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
4

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.
5

Given and , what is ?

Question illustration
A
1.404
B
1.739
C
2.773
D
2.988
6

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
7

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
8

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
9

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.
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

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