AnswersPBCSD_Grade_Forgiveness_1200330_Algebra 2_S2_2024Base e

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15 verified answers
1
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What is written as a single logarithm?

Question illustration
A
4 log Subscript one-half Baseline 2 Superscript 4 Baseline u squared minus v cubed
Option A
B
log Subscript one-half Baseline w Superscript 4 Baseline (StartFraction u squared Over v cubed EndFraction)
Option B
C
log Subscript one-half Baseline (StartFraction w Superscript 4 Baseline Over u squared v cubed EndFraction)
Option C
D
log Subscript one-half Baseline (w (StartFraction u squared Over v cubed EndFraction)) Superscript 4
Option D
2
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The intensity, or loudness, of a sound can be measured in decibels (dB), according to the equation , where I is the intensity of a given sound and I0 is the threshold of hearing intensity. What is the intensity, in decibels, [I(dB)], when ?

Question illustration
A
15
B
32
C
320
D
737
3

Which function is shown in the graph below?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
4

Which of the following shows the extraneous solution to the logarithmic equation below?

Question illustration
A
x = negative 6
Option A
B
x = negative 4
Option B
C
x = negative 2
Option C
D
x = negative 1
Option D
5

The two expressions below have the same value when rounded to the nearest hundredth.What is the approximate value of to the nearest hundredth?

Question illustration
A
0.93
B
1.23
C
9.16
D
65.53
6

What are the solutions to

Question illustration
A
x = negative 2 and x = negative 4
Option A
B
x = negative 1 and x = 8
Option B
C
x = 1 and x = negative 8
Option C
D
x = 2 and x = 4
Option D
7

Identify the equation that translates five units down.

Question illustration
A
y = l n (x minus 5)
Option A
B
y = l n (x) + 5
Option B
C
y = l n (x + 5)
Option C
D
y = l n (x) minus 5
Option D
8

Which of the following shows the graph of

Question illustration
A
On a coordinate plane, a curve approaches the y-axis in quadrant 3. It increases into quadrant 2 and crosses the x-axis at (negative 0.5, 0).
Option A
B
On a coordinate plane, a curve approaches the y-axis in quadrant 3. It increases into quadrant 2 and crosses the x-axis at (negative 4, 0).
Option B
C
On a coordinate plane, a curve approaches the y-axis in quadrant 4. It increases into quadrant 1 and crosses the x-axis at (0.5, 0).
Option C
D
On a coordinate plane, a curve approaches the y-axis in quadrant 4. It increases into quadrant 1 and crosses the x-axis at (4, 0).
Option D
9

What is rewritten using the power property?

Question illustration
A
e log Subscript 6 Baseline f
Option A
B
f log Subscript 6 Baseline e
Option B
C
log Subscript 6 Baseline (e times f)
Option C
D
log Subscript 6 Baseline (e + f)
Option D
10

The magnitude, M, of an earthquake is defined to be , where I is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and S is the intensity of a “standard” earthquake, which is barely detectable. What is the magnitude of an earthquake that is 1,000 times more intense than a standard earthquake? Use a calculator. Round your answer to the nearest tenth.

Question illustration
A
2
B
3
C
4.5
D
6.9
11

Which equation has x = 4 as the solution?

A
log Subscript 4 Baseline (3 x + 4) = 2
Option A
B
log Subscript 3 Baseline (2 x minus 5) = 2
Option B
C
log Subscript x Baseline 64 = 4
Option C
D
log Subscript x Baseline 16 = 4
Option D
12

What is the true solution to the logarithmic equation?

Question illustration
A
mc026-2.jpg
Option A
B
mc026-3.jpg
Option B
C
mc026-4.jpg
Option C
D
mc026-5.jpg
Option D
13

Which expression is equivalent to ?

Question illustration
A
log Subscript 2 Baseline 9 + 3 log Subscript 2 Baseline x
Option A
B
log Subscript 2 Baseline x + 3 log Subscript 2 Baseline 9
Option B
C
3 log Subscript 2 Baseline x minus log Subscript 2 Baseline 9
Option C
D
3 log Subscript 2 Baseline 9 minus log Subscript 2 Baseline x
Option D
14

A student showed the steps below while solving the equation by graphing.Step 1:Write a system of equations: Step 2: Use the change of base formula to rewrite the equations:Step 3:Graph the two equations:Step 4:Identify the x-value at the point of intersection:In which step did the student make the first error?

Question illustration
A
step 1
B
step 2
C
step 3
D
step 4
15

What is the domain of the function

Question illustration
A
x less-than negative 2
Option A
B
x greater-than negative 2
Option B
C
x less-than 2
Option C
D
x greater-than 2
Option D

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