Question 1

Use the Definition of a Logarithm to Solve Logarithmic Equations
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic
expressions. Give the exact answer.
- log⁡6(x−1) =−3\log _ { 6 } ( x - 1 )  = - 3log6​(x−1) =−3

Accepted Answer

A)    {217216}\left\{ \frac { 217 } { 216 } \right\}{216217​} 
B)    {−215216}\left\{ - \frac { 215 } { 216 } \right\}{−216215​} 
C)    {217729}\left\{ \frac { 217 } { 729 } \right\}{729217​} 
D)    {−215729}\left\{ - \frac { 215 } { 729 } \right\}{−729215​}E) B) and C)
F) All of the above

Question 2

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places
- log⁡0.417\log _ { 0.4 } 17log0.4​17

Accepted Answer

A)    −3.0920- 3.0920−3.0920 
B)    −0.3234- 0.3234−0.3234 
C)    0.83250.83250.8325 
D)    1.62841.62841.6284E) C) and D)
F) A) and B)

Question 3

Evaluate the expression without using a calculator.
- log⁡4116\log _ { 4 } \frac { 1 } { 16 }log4​161​

Accepted Answer

A)    −2- 2−2 
B)   8
C)    12\frac { 1 } { 2 }21​ 
D)   2 E) A) and D)
F) B) and C)

Question 4

Solve the problem.
-The population of a certain country is growing at a rate of  1.2%1.2 \%1.2%  per year. How long will it take for this country's population to double? Use the formula  t=ln⁡2kt = \frac { \ln 2 } { k }t=kln2​ , which gives the time,  ttt , for a population with growth rate  kkk , to double. (Round to the nearest whole year.)

Accepted Answer

A)   58 years
B)   59 years
C)   60 years
D)   57 years E) A) and C)
F) C) and D)

Question 5

Use the Definition of a Logarithm to Solve Logarithmic Equations
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic
expressions. Give the exact answer.
- ln⁡x+8=7\ln \sqrt { x + 8 } = 7lnx+8​=7

Accepted Answer

A)    {e14−8}\left\{ \mathrm { e } ^ { 14 } - 8 \right\}{e14−8} 
B)    {e14+8}\left\{ \mathrm { e } ^ { 14 } + 8 \right\}{e14+8} 
C)    {e72+8}\left\{ \frac { \mathrm { e } ^ { 7 } } { 2 } + 8 \right\}{2e7​+8} 
D)    {e7−8}\left\{ e ^ { 7 } - 8 \right\}{e7−8}E) All of the above
F) A) and D)

Question 6

Use the One-to-One Property of Logarithms to Solve Logarithmic Equations
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic
expressions. Give the exact answer.
- ln⁡(x−5) −ln⁡(x+7) =ln⁡(x−6) −ln⁡(x+1) \ln ( x - 5 )  - \ln ( x + 7 )  = \ln ( x - 6 )  - \ln ( x + 1 ) ln(x−5) −ln(x+7) =ln(x−6) −ln(x+1)

Accepted Answer

A)    {375}\left\{ \frac { 37 } { 5 } \right\}{537​} 
B)    {−375}\left\{ - \frac { 37 } { 5 } \right\}{−537​} 
C)    {475}\left\{ \frac { 47 } { 5 } \right\}{547​} 
D)    ∅\varnothing∅E) All of the above
F) A) and C)

Question 7

Graph the function.
-Use the graph of  f(x) =ln⁡xf ( x )  = \ln xf(x) =lnx  to obtain the graph of  g(x) =3ln⁡xg ( x )  = 3 \ln xg(x) =3lnx .

Accepted Answer

A)  
B)  
C)  
D)   E) C) and D)
F) None of the above

Question 8

Solve the problem.
-The function  f(x) =1+1.5ln⁡(x+1) f ( x )  = 1 + 1.5 \ln ( x + 1 ) f(x) =1+1.5ln(x+1)   models the average number of free-throws a basketball player can make consecutively during practice as a function of time, where  xxx  is the number of consecutive days the basketball player has practiced for two hours. After how many days of practice can the basketball player make an average of 6 consecutive free throws?

Accepted Answer

A)   27 days
B)   29 days
C)   105 days
D)   107 days E) B) and D)
F) A) and B)

Question 9

Solve the problem.
-The logistic growth function  f(t) =7201+9.3e−0.12tf ( t )  = \frac { 720 } { 1 + 9.3 e ^ { - 0.12 t } }f(t) =1+9.3e−0.12t720​  describes the population of a species of butterflies t months after they are introduced to a non-threatening habitat. How many butterflies were initially introduced to the habitat?

Accepted Answer

A)   70 butterflies
B)   720 butterflies
C)   9 butterflies
D)   2 butterflies E) C) and D)
F) B) and D)

Question 10

Find the domain of the logarithmic function.
- f(x) =ln⁡(6−x) f ( x )  = \ln ( 6 - x ) f(x) =ln(6−x)

Accepted Answer

A)    (−∞,6) ( - \infty , 6 ) (−∞,6)  
B)    (−∞,0) ( - \infty , 0 ) (−∞,0)  
C)    (−6,∞) ( - 6 , \infty ) (−6,∞)  
D)    (−∞,6) ( - \infty , 6 ) (−∞,6)   or  (6,∞) ( 6 , \infty ) (6,∞) E) A) and D)
F) B) and D)

Question 11

Model Exponential Growth and Decay
Solve.
-The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by
The exponential growth model A = 9400e0.061t. By what percentage is the account increasing each year?

Accepted Answer

A)  6.1%
B)  6.5%
C)  6.7%
D)  6.8%E) A) and B)
F) B) and D)

Question 12

Graph the function.
-Use the graph of  f(x) =ln⁡xf ( x )  = \ln xf(x) =lnx  to obtain the graph of  g(x) =4−ln⁡xg ( x )  = 4 - \ln xg(x) =4−lnx .

Accepted Answer

A)  
B)  
C)  
D)   E) All of the above
F) B) and D)

Question 13

Use the Product Rule
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
- log⁡6(7⋅3) \log _ { 6 } ( 7 \cdot 3 ) log6​(7⋅3)

Accepted Answer

A)    log⁡67+log⁡63\log _ { 6 } 7 + \log _ { 6 } 3log6​7+log6​3 
B)    log⁡67−log⁡63\log _ { 6 } 7 - \log _ { 6 } 3log6​7−log6​3 
C)    log⁡621\log _ { 6 } 21log6​21 
D)    (log⁡67) (log⁡63) \left( \log _ { 6 } 7 \right)  \left( \log _ { 6 } 3 \right) (log6​7) (log6​3) E) A) and B)
F) All of the above

Question 14

Find the domain of the logarithmic function.
- f(x) =log⁡(x2−8x+12) f ( x )  = \log \left( x ^ { 2 } - 8 x + 12 \right) f(x) =log(x2−8x+12)

Accepted Answer

A)    (−∞,2) ∪(6,∞) ( - \infty , 2 )  \cup ( 6 , \infty ) (−∞,2) ∪(6,∞)  
B)    (−2,6) ( - 2,6 ) (−2,6)  
C)    (6,∞) ( 6 , \infty ) (6,∞)  
D)    (−∞,−2) ( - \infty , - 2 ) (−∞,−2)   ( E) A) and B)
F) B) and D)

Question 15

Graph the function.
-Use the graph of  log⁡5x\log _ { 5 } xlog5​x  to obtain the graph of  f(x) =12log⁡5xf ( x )  = \frac { 1 } { 2 } \log _ { 5 } xf(x) =21​log5​x .

Accepted Answer

A)  
B)  
C)  
D)   Graph the functions in the same rectangular coordinate system. E) A) and C)
F) A) and B)

Question 16

Solve the exponential equation. Express the solution set in terms of natural logarithms.
- 39x=2.33 ^ { 9 x } = 2.339x=2.3

Accepted Answer

A)    {ln⁡2.39ln⁡3}\left\{ \frac { \ln 2.3 } { 9 \ln 3 } \right\}{9ln3ln2.3​} 
B)    {ln⁡2.33ln⁡9}\left\{ \frac { \ln 2.3 } { 3 \ln 9 } \right\}{3ln9ln2.3​} 
C)    {9ln⁡2.3ln⁡3}\left\{ \frac { 9 \ln 2.3 } { \ln 3 } \right\}{ln39ln2.3​} 
D)    {2.3ln⁡9ln⁡3}\left\{ \frac { 2.3 \ln 9 } { \ln 3 } \right\}{ln32.3ln9​}E) A) and C)
F) A) and B)

Question 17

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
- log⁡4(x2y6) \log _ { 4 } \left( \frac { x ^ { 2 } } { y ^ { 6 } } \right) log4​(y6x2​)

Accepted Answer

A)    2log⁡4x−6log⁡4y2 \log _ { 4 } x - 6 \log _ { 4 } y2log4​x−6log4​y 
B)    2log⁡4x+6log⁡4y2 \log _ { 4 } x + 6 \log _ { 4 } y2log4​x+6log4​y 
C)    13log⁡4(xy) \frac { 1 } { 3 } \log _ { 4 } \left( \frac { \mathrm { x } } { \mathrm { y } } \right) 31​log4​(yx​)  
D)    6log⁡4y−2log⁡4x6 \log _ { 4 } y - 2 \log _ { 4 } x6log4​y−2log4​xE) B) and C)
F) A) and B)

Question 18

Use the Quotient Rule
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
- ln⁡(e35) \ln \left( \frac { e ^ { 3 } } { 5 } \right) ln(5e3​)

Accepted Answer

A)    3−ln⁡53 - \ln 53−ln5 
B)    ln⁡e3−ln⁡5\ln e ^ { 3 } - \ln 5lne3−ln5 
C)    3+ln⁡53 + \ln 53+ln5 
D)    ln⁡e3+ln⁡5\ln e ^ { 3 } + \ln 5lne3+ln5E) B) and D)
F) C) and D)

Question 19

Solve the equation by expressing each side as a power of the same base and then equating exponents.
- 3x=273 x = 273x=27

Accepted Answer

A)    {3}\{ 3 \}{3} 
B)    {9}\{ 9 \}{9} 
C)    {4}\{ 4 \}{4} 
D)    {2}\{ 2 \}{2}E) A) and B)
F) None of the above

Question 20

Approximate the number using a calculator. Round your answer to three decimal places.
- e−2.1\mathrm { e } ^ { - 2.1 }e−2.1

Accepted Answer

A)    0.1220.1220.122 
B)    −5.708- 5.708−5.708 
C)    −0.122- 0.122−0.122 
D)    0.4220.4220.422E) B) and D)
F) A) and B)

Exam 4: Exponential and Logarithmic Functions

Correct Answer
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Use the Definition of a Logarithm to Solve Logarithmic Equations Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. - $\ln \sqrt { x + 8 } = 7$

Correct Answer
verified

Solve the exponential equation. Express the solution set in terms of natural logarithms. - $3 ^ { 9 x } = 2.3$

Correct Answer
verified

Find the domain of the logarithmic function. - $f ( x ) = \log \left( x ^ { 2 } - 8 x + 12 \right)$

Correct Answer
verified

Correct Answer
verified

Use the Quotient Rule Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\ln \left( \frac { e ^ { 3 } } { 5 } \right)$

Correct Answer
verified

Find the domain of the logarithmic function. - $f ( x ) = \ln ( 6 - x )$

Correct Answer
verified

Use the Product Rule Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 6 } ( 7 \cdot 3 )$

Correct Answer
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Solve the problem. -The logistic growth function $f ( t ) = \frac { 720 } { 1 + 9.3 e ^ { - 0.12 t } }$ describes the population of a species of butterflies t months after they are introduced to a non-threatening habitat. How many butterflies were initially introduced to the habitat?

Correct Answer
verified

Solve the equation by expressing each side as a power of the same base and then equating exponents. - $3 x = 27$

Correct Answer
verified

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 4 } \left( \frac { x ^ { 2 } } { y ^ { 6 } } \right)$

Correct Answer
verified

Graph the function. -Use the graph of $f ( x ) = \ln x$ to obtain the graph of $g ( x ) = 3 \ln x$ . $Graph the function. -Use the graph of f ( x ) = \ln x to obtain the graph of g ( x ) = 3 \ln x . A) B) C) D)$

Correct Answer
verified

Correct Answer
verified

Approximate the number using a calculator. Round your answer to three decimal places. - $\mathrm { e } ^ { - 2.1 }$

Correct Answer
verified

Evaluate the expression without using a calculator. - $\log _ { 4 } \frac { 1 } { 16 }$

Correct Answer
verified

Graph the function. -Use the graph of $f ( x ) = \ln x$ to obtain the graph of $g ( x ) = 4 - \ln x$ . $Graph the function. -Use the graph of f ( x ) = \ln x to obtain the graph of g ( x ) = 4 - \ln x . A) B) C) D)$

Correct Answer
verified

Correct Answer
verified

Use the One-to-One Property of Logarithms to Solve Logarithmic Equations Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. - $\ln ( x - 5 ) - \ln ( x + 7 ) = \ln ( x - 6 ) - \ln ( x + 1 )$

Correct Answer
verified

Use the Definition of a Logarithm to Solve Logarithmic Equations Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. - $\log _ { 6 } ( x - 1 ) = - 3$

Correct Answer
verified

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places - $\log _ { 0.4 } 17$

Correct Answer
verified

Exam 4: Exponential and Logarithmic Functions

Correct AnswerverifiedShow Answer

Use the Definition of a Logarithm to Solve Logarithmic Equations Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. - ln⁡x+8=7\ln \sqrt { x + 8 } = 7lnx+8​=7

Correct AnswerverifiedShow Answer

Solve the exponential equation. Express the solution set in terms of natural logarithms. - 39x=2.33 ^ { 9 x } = 2.339x=2.3

Correct AnswerverifiedShow Answer

Find the domain of the logarithmic function. - f(x) =log⁡(x2−8x+12) f ( x ) = \log \left( x ^ { 2 } - 8 x + 12 \right) f(x) =log(x2−8x+12)

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Use the Quotient Rule Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - ln⁡(e35) \ln \left( \frac { e ^ { 3 } } { 5 } \right) ln(5e3​)

Correct AnswerverifiedShow Answer

Find the domain of the logarithmic function. - f(x) =ln⁡(6−x) f ( x ) = \ln ( 6 - x ) f(x) =ln(6−x)

Correct AnswerverifiedShow Answer

Use the Product Rule Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡6(7⋅3) \log _ { 6 } ( 7 \cdot 3 ) log6​(7⋅3)

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Solve the equation by expressing each side as a power of the same base and then equating exponents. - 3x=273 x = 273x=27

Correct AnswerverifiedShow Answer

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡4(x2y6) \log _ { 4 } \left( \frac { x ^ { 2 } } { y ^ { 6 } } \right) log4​(y6x2​)

Correct AnswerverifiedShow Answer

Graph the function. -Use the graph of f(x) =ln⁡xf ( x ) = \ln xf(x) =lnx to obtain the graph of g(x) =3ln⁡xg ( x ) = 3 \ln xg(x) =3lnx .

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Approximate the number using a calculator. Round your answer to three decimal places. - e−2.1\mathrm { e } ^ { - 2.1 }e−2.1

Correct AnswerverifiedShow Answer

Evaluate the expression without using a calculator. - log⁡4116\log _ { 4 } \frac { 1 } { 16 }log4​161​

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Graph the function. -Use the graph of f(x) =ln⁡xf ( x ) = \ln xf(x) =lnx to obtain the graph of g(x) =4−ln⁡xg ( x ) = 4 - \ln xg(x) =4−lnx .

Correct AnswerverifiedShow Answer

Graph the function. -Use the graph of log⁡5x\log _ { 5 } xlog5​x to obtain the graph of f(x) =12log⁡5xf ( x ) = \frac { 1 } { 2 } \log _ { 5 } xf(x) =21​log5​x .

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Use the Definition of a Logarithm to Solve Logarithmic Equations Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. - log⁡6(x−1) =−3\log _ { 6 } ( x - 1 ) = - 3log6​(x−1) =−3

Correct AnswerverifiedShow Answer

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places - log⁡0.417\log _ { 0.4 } 17log0.4​17

Correct AnswerverifiedShow Answer

Correct Answer
verified

Use the Definition of a Logarithm to Solve Logarithmic Equations Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. - $\ln \sqrt { x + 8 } = 7$

Correct Answer
verified

Solve the exponential equation. Express the solution set in terms of natural logarithms. - $3 ^ { 9 x } = 2.3$

Correct Answer
verified

Find the domain of the logarithmic function. - $f ( x ) = \log \left( x ^ { 2 } - 8 x + 12 \right)$

Correct Answer
verified

Correct Answer
verified

Use the Quotient Rule Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\ln \left( \frac { e ^ { 3 } } { 5 } \right)$

Correct Answer
verified

Find the domain of the logarithmic function. - $f ( x ) = \ln ( 6 - x )$

Correct Answer
verified

Use the Product Rule Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 6 } ( 7 \cdot 3 )$

Correct Answer
verified

Correct Answer
verified

Solve the equation by expressing each side as a power of the same base and then equating exponents. - $3 x = 27$

Correct Answer
verified

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 4 } \left( \frac { x ^ { 2 } } { y ^ { 6 } } \right)$

Correct Answer
verified

Graph the function. -Use the graph of $f ( x ) = \ln x$ to obtain the graph of $g ( x ) = 3 \ln x$ . $Graph the function. -Use the graph of f ( x ) = \ln x to obtain the graph of g ( x ) = 3 \ln x . A) B) C) D)$

Correct Answer
verified

Correct Answer
verified

Approximate the number using a calculator. Round your answer to three decimal places. - $\mathrm { e } ^ { - 2.1 }$

Correct Answer
verified

Evaluate the expression without using a calculator. - $\log _ { 4 } \frac { 1 } { 16 }$

Correct Answer
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Graph the function. -Use the graph of $f ( x ) = \ln x$ to obtain the graph of $g ( x ) = 4 - \ln x$ . $Graph the function. -Use the graph of f ( x ) = \ln x to obtain the graph of g ( x ) = 4 - \ln x . A) B) C) D)$

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Use the Definition of a Logarithm to Solve Logarithmic Equations Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. - $\log _ { 6 } ( x - 1 ) = - 3$

Correct Answer
verified

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places - $\log _ { 0.4 } 17$

Correct Answer
verified