AnswersCR - Algebra 2 26-27 - S2Solving Logarithmic Equations using Technology

Solving Logarithmic Equations using Technology — Unit test Answers

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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 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
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

For what value of n does ?

Question illustration
A
–3
B
Negative one-third
Option B
C
Five-ninths
Option C
D
1
4

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 35 times more intense than a standard earthquake? Use a calculator. Round your answer to the nearest tenth.

Question illustration
A
–1.5
B
–0.5
C
1.5
D
3.6
5

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
6

What is the simplified value of the exponential expression ?

Question illustration
A
Option
Option A
B
Option
Option B
C
2
D
4
7

Which function is shown in the graph below?

Question illustration
A
y = (one-half) Superscript x + 3 Baseline minus 1
Option A
B
y = (one-half) Superscript x minus 3 Baseline + 1
Option B
C
y = (one-half) Superscript x minus 1 Baseline + 3
Option C
D
y = (one-half) Superscript x + 1 Baseline minus 3
Option D
8

For what value of n does ?

Question illustration
A
–3
B
Negative three-halves
Option B
C
Three-halves
Option C
D
3
9

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
10

Which is equivalent to ?

Question illustration
A
4
B
12
C
64
D
192
11

How does the value of compare with the value of ?

Question illustration
A
The value of is about 4 times the value of .
Option A
B
The value of is about times the value of .
Option B
C
The value of is about 3 times the value of .
Option C
D
The value of is about times the value of .
Option D
12

What is the domain of ?

Question illustration
A
all real numbers less than –3
B
all real numbers greater than –3
C
all real numbers less than 3
D
all real numbers greater than 3
13

What is the approximate value of ?

Question illustration
A
0.233
B
0.557
C
0.620
D
1.796
14

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
15

For what value of x does ?

Question illustration
A
–9
B
–3
C
3
D
9
16

If , what is the value of s?

Question illustration
A
–1
B
0
C
1
D
no solution
17

What is the domain of ?

Question illustration
A
all real numbers less than –3
B
all real numbers greater than –3
C
all real numbers less than 3
D
all real numbers greater than 3
18

Which graph shows the solution to the equation below?

Question illustration
A
On a coordinate plane, 2 curves intersect at (1, 0).
Option A
B
On a coordinate plane, a line intersects with a curve.
Option B
C
On a coordinate plane, a line with positive slope and a curve are shown.
Option C
D
On a coordinate plane, 2 hyperbolas are shown.
Option D
19

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
20

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.

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