AnswersDHS Algebra 2 VSolving Logarithmic Equations using Technology

Properties of Logarithms Answers

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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
2
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Omar wants to use a graph to solve the equation below.Which system of equations should Omar use?

Question illustration
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
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

Tyler applied the change of base formula to a logarithmic expression. The resulting expression is shown below. Which expression could be Tyler’s original expression?

Question illustration
A
Log Subscript one-fourth Baseline 12
Option A
B
Log Subscript 12 Baseline One-fourth
Option B
C
12 Log one-fourth
Option C
D
One-fourth log 12
Option D
5

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
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 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.
8

Which expression can be used to approximate the expression below, for all positive numbers a, b, and x, where a 1 and b 1?

Question illustration
A
StartFraction log Subscript b Baseline x Over log Subscript b Baseline a EndFraction
Option A
B
StartFraction log Subscript b Baseline a Over log Subscript b Baseline x EndFraction
Option B
C
StartFraction log Subscript a Baseline b Over log Subscript x Baseline b EndFraction
Option C
D
StartFraction log Subscript a Baseline x Over log Subscript b Baseline x EndFraction
Option D
9

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

Question illustration
A
–1.613
B
–1.522
C
0.585
D
3.079
10

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

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