AnswersDHS Algebra 2 VSolving Logarithmic Equations using Technology

Solving Logarithmic Equations using Technology — Unit test Answers

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1
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What is the rate of increase for the function f(x) = ?

Question illustration
A
One-third
Option A
B
2
Option B
C
4
D
4
Option D
2
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What are the domain and range of ?

Question illustration
d
domain: x > 1; range: y > 2
d
domain: x > 1; range: all real numbers
d
domain: all real numbers; range: y > 1
d
domain: all real numbers; range: all real numbers
3

For what value of x does ?

Question illustration
A
1
B
2
C
4
D
5
4

Which is the graph of ?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
5

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
6

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
7

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
8

Jerome solved the equation below by graphing.Which of the following shows the correct system of equations and solution?

Question illustration
A
; x = 3
Option A
B
; x = 4
Option B
C
; x = 33
Option C
D
; x = 44
Option D
9

If , what is the value of x?

Question illustration
A
Five-eighths
Option A
B
Eight-fifths
Option B
C
2
D
8
10

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
11

Which function has a horizontal asymptote of y = 3?

f
f(x) = 3(2x)
f
f(x) = 2(4)x–3
f
f(x) = 2(3x)
f
f(x) = 2(4x) + 3
12

Which function has a simplified base of 4?

Question illustration
A
f(x) = 2
Option A
B
f(x) = 2
Option B
C
f(x) = 4
Option C
D
f(x) = 4
Option D
13

If , what is the value of x?

Question illustration
A
–3
B
–2
C
2
D
3
14

If you are given the graph of , how could you graph ?

Question illustration
T
Translate each point of the graph of g(x) 5 units up.
T
Translate each point of the graph of g(x) 5 units down.
T
Translate each point of the graph of g(x) 5 units left.
T
Translate each point of the graph of g(x) 5 units right.
15

What is the solution of ?

Question illustration
A
6
B
9
C
18
D
81
16

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
17

If , what is the value of x?

Question illustration
A
–3
B
–2
C
2
D
3
18

What are the domain and range of ?

Question illustration
A
domain: x > 1; range: y > 2
B
domain: x > 1; range: all real numbers
C
domain: all real numbers; range: y > 1
D
domain: all real numbers; range: all real numbers
19

For what values of x does ?

Question illustration
A
x = –3, x = 1
B
x = –1, x = 3
C
x = negative three-halves, x = 2
Option C
D
x = negative 2, x = three-halves
Option D
20

What is the range of the function f(x) = –2(6x) + 3?

A
(negative infinity, negative 2 Right-bracket
Option A
B
(negative infinity, 3)
Option B
C
Left-bracket negative 2, infinity)
Option C
D
Left-bracket 3, infinity)
Option D

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