AnswersPBCSD_Grade_Forgiveness_1200330_Algebra 2_S2_2024Properties of Logarithms

Properties of Logarithms Answers

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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.
2
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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
3

Given and , what is ?

Question illustration
A
1.404
B
1.739
C
2.773
D
2.988
4

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
5

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
6

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
7

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
8

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
9

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
10

Given and , what is ?

Question illustration
A
1.118
B
1.893
C
2.402
D
3.542

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