AnswersAZ-Common Core Algebra II BSolving Logarithmic Equations using Technology

Solving Logarithmic Equations using Technology Answers

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1
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Omar wants to use a graph to solve the equation below.Which system of equations should Omar use?

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A
y 1 = StartFraction log 6 Over x EndFraction , y 2 = StartFraction log 2 Over x + 4 EndFraction
Option A
B
y 1 = StartFraction log x Over log 6 EndFraction, y 2 = StartFraction log x + 4 Over log 2 EndFraction
Option B
C
y 1 = StartFraction log 6 Over log 2 EndFraction, y 2 = StartFraction log x Over log (x + 4) EndFraction
Option C
D
y 1 = StartFraction log x Over log 6 EndFraction, y 2 = StartFraction log (x + 4) Over log 2 EndFraction
Option D
2
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Consider the equation below.Which system of equations can represent the equation?

Question illustration
A
y 1 = StartFraction log (x + 3) Over log 4 EndFraction, y 2 = StartFraction log (2 + x) Over log 2 EndFraction
Option A
B
y 1 = StartFraction log x + 3 Over log 4 EndFraction, y 2 = StartFraction log 2 + x Over log 2 EndFraction
Option B
C
y 1 = StartFraction log 4 Over log 2 EndFraction, y 2 = StartFraction log (x + 3) Over log (2 + x) EndFraction
Option C
D
y 1 = StartFraction log x + 3 Over 4 EndFraction, y 2 = StartFraction log 2 + x Over 2 EndFraction
Option D
3

What is the approximate value of x in the equation below?

Question illustration
A
–2.523
B
–1.317
C
2.880
D
7.485
4

Devonte used the change of base formula to approximate . Which expression did Devonte use?

Question illustration
A
Log StartFraction 8 Over 25 EndFraction
Option A
B
StartFraction log 8 Over log 25 EndFraction
Option B
C
log StartFraction 25 Over 8 EndFraction
Option C
D
StartFraction log 25 Over log 8 EndFraction
Option D
5

Which is equivalent to ?

Question illustration
A
log n = StartFraction log 2 Over 4 EndFraction
Option A
B
n = StartFraction log 2 Over log 4 EndFraction
Option B
C
n = log 4 times log 2
Option C
D
log n = 4 log 2
Option D
6

Which expression results when the change of base formula is applied to ?

Question illustration
A
StartFraction log (x + 2) Over log 4 EndFraction
Option A
B
StartFraction log 4 Over log (x + 2) EndFraction
Option B
C
StartFraction log 4 Over log x + 2 EndFraction
Option C
D
StartFraction log x + 2 Over log 4 EndFraction
Option D
7

A teacher used the change of base formula to determine whether the equation below is correct.Which statement explains whether the equation is correct?

Question illustration
A
The equation is correct since (log Subscript 2 Baseline 10) (log Subscript 4 Baseline 8) (log Subscript 10 Baseline 4) = log (2 times 10) times log (4 times 8) times log (10 times 4). = log (20) times log (32) times log (40). =3
Option A
B
The equation is correct since (log Subscript 2 Baseline 10) (log Subscript 4 Baseline 8) (log Subscript 10 Baseline 4) = StartFraction log 10 Over log 2 EndFraction times StartFraction log 8 Over log 4 EndFraction times StartFraction log 4 Over log 10 EndFraction. = StartFraction log 8 Over log 2 EndFraction. = 3
Option B
C
The equation is correct since (log Subscript 2 Baseline 10) (log Subscript 4 Baseline 8) (log Subscript 10 Baseline 4) = StartFraction log 10 Over log 2 EndFraction times StartFraction log 8 Over log 4 EndFraction times StartFraction log 4 Over log 10 EndFraction. = StartFraction log 8 Over log 2 EndFraction. = 4.
Option C
D
The equation is not correct since (log Subscript 2 Baseline 10) (log Subscript 4 Baseline 8) (log Subscript 10 Baseline 4) = log StartFraction 10 Over 2 EndFraction times log eight-fourths times log four-tenths. = log 5 times log 2 times log 0.4. = negative 0.08
Option D
8

What is the approximate value of x in the equation below.

Question illustration
A
–3.396
B
–0.708
C
0.304
D
0.955
9

A student solved the equation below by graphing.Which statement about the graph is true?

Question illustration
A
The curves do not intersect.
B
The curves intersect at one point.
C
The curves intersect at two points.
D
The curves appear to coincide.
10

Kim solved the equation below by graphing a system of equations.What is the approximate solution to the equation?

Question illustration
A
0.6
B
0.9
C
1.4
D
1.6

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