AnswersPBCSD_Grade_Forgiveness_1200330_Algebra 2_S2_2024Solving Exponential and Logarithmic Equations

Solving Exponential and Logarithmic Equations — Test Answers

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1
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If , what is the value of s?

Question illustration
A
–1
B
0
C
1
D
no solution
2
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Which of the following is true about the base b of a logarithmic function?

A
b > 0 and b = 1
B
b > 0 and
Option B
C
b < 0 and
Option C
D
b < 0 and b = 1
3

Which of the following shows the graph of y = 4x + 3?

A
On a coordinate plane, an exponential function starts at y = 3 in quadrant 2 and then increases rapidly into quadrant 1.
Option A
B
On a coordinate plane, an exponential function starts at y = 0 in quadrant 2 and then increases rapidly in quadrant 2.
Option B
C
On a coordinate plane, an exponential function starts at y = 0 in quadrant 2 and then increases rapidly into quadrant 1.
Option C
D
On a coordinate plane, an exponential function starts at y = negative 3 in quadrant 3 and then increases rapidly into quadrant 1.
Option D
4

What is the true solution to the equation below?

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

Devon purchased a new car valued at $16,000 that depreciated continuously at a rate of 35%. Its current value is $2,000. The equation represents the situation, where t is the age of the car in years and r is the rate of depreciation. About how old is Devon’s car? Use a calculator and round your answer to the nearest whole number.

Question illustration
A
1 year
B
2 years
C
5 years
D
8 years
6

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

Question illustration
A
Translate each point of the graph of h(x) 3 units up.
B
Translate each point of the graph of h(x) 3 units down.
C
Translate each point of the graph of h(x) 3 units right.
D
Translate each point of the graph of h(x) 3 units left.
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. Jessica is listening to soft music at a sound intensity level of 10-9 on her computer while she does her homework. Braylee is completing her homework while listening to very loud music at a sound intensity level of 10-3 on her headphones. How many times louder is Braylee’s music than Jessica’s?

Question illustration
A
times louder
Option A
B
3 times louder
C
30 times louder
D
90 times louder
8

What is the true solution to the equation below?

Question illustration
A
x = 2
Option A
B
x = 4
Option B
C
x = 8
Option C
D
x = 64
Option D
9

Which expression is equivalent to ?

Question illustration
A
4 log Subscript 12 Baseline x + one-half log Subscript 12 Baseline (x cubed minus 2) minus 5 log Subscript 12 Baseline (x times 1)
Option A
B
4 log Subscript 12 Baseline x + one-half log Subscript 12 Baseline StartFraction x cubed Over 2 EndFraction minus 5 log Subscript 12 Baseline 1
Option B
C
log Subscript 12 Baseline 4 x + one-half log Subscript 12 Baseline (x cubed minus 2) minus 5 log Subscript 12 Baseline (x) + 1
Option C
D
4 log Subscript 12 Baseline x + one-half log Subscript 12 Baseline (x cubed minus 2) minus 5 log Subscript 12 Baseline (x + 1)
Option D
10

For what value of x does ?

Question illustration
A
–9
B
–3
C
3
D
9
11

Which graph represents an exponential decay function?

A
On a coordinate plane, a curve opens up and to the right in quadrant 4.
Option A
B
On a coordinate plane, a curve opens up and to the right in quadrants 1 and 2. The line rapidly decreases in quadrant 2 and then curves and approaches the x-axis in quadrant 1.
Option B
C
On a coordinate plane, a line slightly curves up in quadrant 1.
Option C
D
On a coordinate plane, a line slowly increases in quadrant 2 and then increases rapidly into quadrant 1.
Option D
12

What is the solution to

Question illustration
A
x = negative 4
Option A
B
x = negative 2
Option B
C
x = 4
Option C
D
x = 8
Option D
13

What is the range of the function

Question illustration
A
all real numbers less than –1
B
all real numbers greater than –1
C
all real numbers less than 1
D
all real numbers greater than 1
14

What is the solution to

Question illustration
A
x = negative 95
Option A
B
x = negative 5
Option B
C
x = 5
Option C
D
x = 95
Option D
15

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 is the threshold of hearing intensity. What is the intensity, in decibels, [I(dB)], when ?

Question illustration
A
8
B
9
C
19
D
80
16

What is the value of ?

Question illustration
A
–4
B
Negative one-fourth
Option B
C
One-fourth
Option C
D
4
17

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 rock concert with a sound intensity of 10–1?

Question illustration
A
2 Db
B
22 Db
C
60 Db
D
110 Db
18

Which equation is represented by the graph below?

Question illustration
A
y = l n x minus 3
Option A
B
y = l n x minus 4
Option B
C
y = e Superscript x Baseline minus 3
Option C
D
y = e Superscript x Baseline minus 4
Option D
19

What is the true solution to the logarithmic equation below?

Question illustration
A
x = 0
Option A
B
x = two-ninths
Option B
C
x = four-ninths
Option C
D
x = two-thirds
Option D
20

Which is the graph of ?

Question illustration
A
On a coordinate plane, a curve starts at y = negative 3 and curves up into quadrant 1. It approaches y = 3.
Option A
B
On a coordinate plane, a curve starts at y = negative 2 and curves up into quadrant 2. It approaches y = 2 in quadrant 2.
Option B
C
On a coordinate plane, a curve starts at y = 3 and curves down into quadrant 4. It approaches y = negative 3 in quadrant 4.
Option C
D
On a coordinate plane, a curve starts at y = 4 and curves down into quadrant 3. It approaches y = negative 3 in quadrant 3.
Option D

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