Question 1

Graph the function.
-Use the graph of  log⁡2x\log _ { 2 } xlog2​x  to obtain the graph of  f(x) =1+log⁡2xf ( x )  = 1 + \log _ { 2 } xf(x) =1+log2​x .

Accepted Answer

A)  
B)  
C)  
D)

Question 2

Find the domain of the logarithmic function.
- f(x) =log⁡5(x−9) 2f ( x )  = \log _ { 5 } ( x - 9 )  ^ { 2 }f(x) =log5​(x−9) 2

Accepted Answer

A)    (−∞,9) ( - \infty , 9 ) (−∞,9)   or  (9,∞) ( 9 , \infty ) (9,∞)  
B)    (−∞,0) ( - \infty , 0 ) (−∞,0)   or  (0,∞) ( 0 , \infty ) (0,∞)  
C)    (−9,∞) ( - 9 , \infty ) (−9,∞)  
D)    (9,∞) ( 9 , \infty ) (9,∞)   (9

Question 3

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm
whose coefficient is 1. Where possible, evaluate logarithmic expressions.
- log⁡3135−log⁡35\log _ { 3 } 135 - \log _ { 3 } 5log3​135−log3​5

Accepted Answer

A)   3
B)    log⁡3675\log _ { 3 } 675log3​675 
C)    log⁡3130\log _ { 3 } 130log3​130 
D)    log⁡31351/5\log _ { 3 } 135 ^ { 1 / 5 }log3​1351/5

Question 4

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm
whose coefficient is 1. Where possible, evaluate logarithmic expressions.
- 6log⁡bq−log⁡br6 \log _ { b } q - \log _ { b } r6logb​q−logb​r

Accepted Answer

A)    log⁡b(q6r) \log _ { \mathrm { b } } \left( \frac { \mathrm { q } ^ { 6 } } { \mathrm { r } } \right) logb​(rq6​)  
B)    log⁡bq6÷log⁡br\log _ { \mathrm { b } } \mathrm { q } ^ { 6 } \div \log _ { \mathrm { b } } \mathrm { r }logb​q6÷logb​r 
C)    log⁡b(q6−r) \log _ { \mathrm { b } } \left( \mathrm { q } ^ { 6 } - \mathrm { r } \right) logb​(q6−r)  
D)    log⁡b(6qr) \log _ { \mathrm { b } } \left( \frac { 6 \mathrm { q } } { \mathrm { r } } \right) logb​(r6q​)

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.
- 3ln⁡(6x) =63 \ln ( 6 x )  = 63ln(6x) =6

Accepted Answer

A)    {e26}\left\{ \frac { e ^ { 2 } } { 6 } \right\}{6e2​} 
B)    {e1/3}\left\{ e ^ { 1 / 3 } \right\}{e1/3} 
C)    {e2}\left\{ e ^ { 2 } \right\}{e2} 
D)    {2ln⁡6}\left\{ \frac { 2 } { \ln 6 } \right\}{ln62​}

Question 6

Graph the function.
-Use the graph of  f(x) =exf ( x )  = e ^ { x }f(x) =ex  to obtain the graph of  g(x) =ex−5g ( x )  = e ^ { x - 5 }g(x) =ex−5

Accepted Answer

A)  
B)  
C)  
D)

Question 7

Write the equation in its equivalent exponential form.
- log⁡b8=3\log _ { b } 8 = 3logb​8=3

Accepted Answer

A)    b3=8b ^ { 3 } = 8b3=8 
B)    3b=83 ^ { b } = 83b=8 
C)    83=b8 ^ { 3 } = b83=b 
D)    8b=38 ^ { b } = 38b=3

Question 8

Solve the problem.
-A sample of  300 g300 \mathrm {~g}300 g  of lead-210 decays to polonium-210 according to the function given by  A(t) =300e−0.032t\mathrm { A } ( \mathrm { t } )  = 300 \mathrm { e } ^ { - 0.032 \mathrm { t } }A(t) =300e−0.032t , where  t\mathrm { t }t  is time in years. What is the amount of the sample after 60 years (to the nearest g) ?

Accepted Answer

A)    44 g44 \mathrm {~g}44 g 
B)    2046 g2046 \mathrm {~g}2046 g 
C)    230 g230 \mathrm {~g}230 g 
D)    32 g32 \mathrm {~g}32 g

Question 9

Graph the function by making a table of coordinates.
- f(x) =(23) xf(x) =\left(\frac{2}{3}\right) ^{x}f(x) =(32​) x

Accepted Answer

A)  
B)  
C)  
D)

Question 10

Solve the problem.
-The long jump record, in feet, at a particular school can be modeled by f(x) = 19.2 + 2.2 ln (x + 1) where x is the number of years since records began to be kept at the school. What is the record for the long jump
20 years after record started being kept? Round your answer to the nearest tenth.

Accepted Answer

A)  25.9 feet
B)  25.8 feet
C)  25.7 feet
D)  21.4 feet

Question 11

Use Natural Logarithms
Evaluate or simplify the expression without using a calculator.
- ln⁡e11\ln \mathrm { e } ^ { 11 }lne11

Accepted Answer

A)   11
B)   e
C)    111\frac { 1 } { 11 }111​ 
D)   1

Question 12

Solve the problem.
-The function  A=A0e−0.0099x\mathrm { A } = \mathrm { A } _ { 0 } \mathrm { e } ^ { - 0.0099 \mathrm { x } }A=A0​e−0.0099x  models the amount in pounds of a particular radioactive material stored in a concrete vault, where  xxx  is the number of years since the material was put into the vault. If 400 pounds of the material are initially put into the vault, how many pounds will be left after 40 years?

Accepted Answer

A)   269 pounds
B)   119 pounds
C)   114 pounds
D)   350 pounds

Question 13

Solve the problem.
-The logistic growth function  f(t) =56,0001+1865.7e−1.9t\mathrm { f } ( \mathrm { t } )  = \frac { 56,000 } { 1 + 1865.7 \mathrm { e } ^ { - 1.9 \mathrm { t } } }f(t) =1+1865.7e−1.9t56,000​  models the number of people who have become ill with a particular infection t weeks after its initial outbreak in a particular community. How many people were ill after 6 weeks?

Accepted Answer

A)   54,854 people
B)   56,000 people
C)   180 people
D)   57,867 people

Question 14

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
- log⁡5(x125) \log _ { 5 } \left( \frac { \sqrt { x } } { 125 } \right) log5​(125x​​)

Accepted Answer

A)    12log⁡5x−3\frac { 1 } { 2 } \log _ { 5 } x - 321​log5​x−3 
B)    15−12log⁡5x15 - \frac { 1 } { 2 } \log _ { 5 } x15−21​log5​x 
C)    log⁡5x−3\log _ { 5 } x - 3log5​x−3 
D)    −3log⁡5x- 3 \log _ { 5 } x−3log5​x

Question 15

Evaluate or simplify the expression without using a calculator.
- 10log⁡610 \log 610log6

Accepted Answer

A)   6
B)    1,000,0001,000,0001,000,000 
C)   60
D)    0.0000010.0000010.000001

Question 16

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⁡4x+log⁡4(x−15) =2\log _ { 4 } x + \log _ { 4 } ( x - 15 )  = 2log4​x+log4​(x−15) =2

Accepted Answer

A)    {16}\{ 16 \}{16} 
B)    {4}\{ 4 \}{4} 
C)    {1,−16}\{ 1 , - 16 \}{1,−16} 
D)    {−1,16}\{ - 1,16 \}{−1,16}

Question 17

Rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm, and then round to three
decimal places.
- y=400(3.8) xy = 400 ( 3.8 )  ^ { x }y=400(3.8) x

Accepted Answer

A)    y=400exln⁡3.8,y=400e1.335xy = 400 \mathrm { e } ^ { x \ln 3.8 } , \mathrm { y } = 400 \mathrm { e } ^ { 1.335 \mathrm { x } }y=400exln3.8,y=400e1.335x 
B)    y=3.8exln⁡400,y=3.8e5.991xy = 3.8 \mathrm { e } ^ { x } \ln 400 , y = 3.8 \mathrm { e } ^ { 5.991 x }y=3.8exln400,y=3.8e5.991x 
C)    y=400e3.8x,y=4002.7181.335x\mathrm { y } = 400 \mathrm { e } ^ { 3.8 \mathrm { x } } , \mathrm { y } = 4002.718 ^ { 1.335 \mathrm { x } }y=400e3.8x,y=4002.7181.335x

Question 18

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places,
for the solution.
- e5x−8−10=1178\mathrm { e } ^ { 5 \mathrm { x } - 8 } - 10 = 1178e5x−8−10=1178

Accepted Answer

A)    3.023.023.02 
B)    2.212.212.21 
C)    1.421.421.42 
D)    0.610.610.61

Question 19

Write the equation in its equivalent logarithmic form.
- 13x=16913 ^ { x } = 16913x=169

Accepted Answer

A)    log⁡13169=x\log _ { 13 } 169 = xlog13​169=x 
B)    log⁡x169=13\log _ { \mathrm { x } } 169 = 13logx​169=13 
C)    log⁡16913=x\log _ { 169 } 13 = xlog169​13=x 
D)    log⁡169x=13\log _ { 169 } x = 13log169​x=13

Question 20

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places,
for the solution.
- ex=3.9\mathrm { e } ^ { \mathrm { x } } = 3.9ex=3.9

Accepted Answer

A)    1.361.361.36 
B)    0.590.590.59 
C)    49.5249.5249.52 
D)    10.6110.6110.61

Exam 4: Exponential and Logarithmic Functions

Find the domain of the logarithmic function. - $f ( x ) = \log _ { 5 } ( x - 9 ) ^ { 2 }$

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. - $\log _ { 4 } x + \log _ { 4 } ( x - 15 ) = 2$

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. - $\log _ { 5 } \left( \frac { \sqrt { x } } { 125 } \right)$

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Evaluate or simplify the expression without using a calculator. - $10 \log 6$

Correct Answer
verified

Use Natural Logarithms Evaluate or simplify the expression without using a calculator. - $\ln \mathrm { e } ^ { 11 }$

Correct Answer
verified

Correct Answer
verified

Write the equation in its equivalent logarithmic form. - $13 ^ { x } = 169$

Correct Answer
verified

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $\mathrm { e } ^ { 5 \mathrm { x } - 8 } - 10 = 1178$

Correct Answer
verified

Correct Answer
verified

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $6 \log _ { b } q - \log _ { b } r$

Correct Answer
verified

Graph the function by making a table of coordinates. - $f(x) =\left(\frac{2}{3}\right) ^{x}$ $Graph the function by making a table of coordinates. - f(x) =\left(\frac{2}{3}\right) ^{x} A) B) C) D)$

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. - $3 \ln ( 6 x ) = 6$

Correct Answer
verified

Graph the function. -Use the graph of $\log _ { 2 } x$ to obtain the graph of $f ( x ) = 1 + \log _ { 2 } x$ . $Graph the function. -Use the graph of \log _ { 2 } x to obtain the graph of f ( x ) = 1 + \log _ { 2 } x . A) B) C) D)$

Correct Answer
verified

Graph the function. -Use the graph of $f ( x ) = e ^ { x }$ to obtain the graph of $g ( x ) = e ^ { x - 5 }$ $Graph the function. -Use the graph of f ( x ) = e ^ { x } to obtain the graph of g ( x ) = e ^ { x - 5 } A) B) C) D)$

Correct Answer
verified

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $\mathrm { e } ^ { \mathrm { x } } = 3.9$

Correct Answer
verified

Rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm, and then round to three decimal places. - $y = 400 ( 3.8 ) ^ { x }$

Correct Answer
verified

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $\log _ { 3 } 135 - \log _ { 3 } 5$

Correct Answer
verified

Write the equation in its equivalent exponential form. - $\log _ { b } 8 = 3$

Correct Answer
verified

Exam 4: Exponential and Logarithmic Functions

Find the domain of the logarithmic function. - f(x) =log⁡5(x−9) 2f ( x ) = \log _ { 5 } ( x - 9 ) ^ { 2 }f(x) =log5​(x−9) 2

Correct AnswerverifiedShow Answer

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⁡5(x125) \log _ { 5 } \left( \frac { \sqrt { x } } { 125 } \right) log5​(125x​​)

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Evaluate or simplify the expression without using a calculator. - 10log⁡610 \log 610log6

Correct AnswerverifiedShow Answer

Use Natural Logarithms Evaluate or simplify the expression without using a calculator. - ln⁡e11\ln \mathrm { e } ^ { 11 }lne11

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Write the equation in its equivalent logarithmic form. - 13x=16913 ^ { x } = 16913x=169

Correct AnswerverifiedShow Answer

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - e5x−8−10=1178\mathrm { e } ^ { 5 \mathrm { x } - 8 } - 10 = 1178e5x−8−10=1178

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - 6log⁡bq−log⁡br6 \log _ { b } q - \log _ { b } r6logb​q−logb​r

Correct AnswerverifiedShow Answer

Graph the function by making a table of coordinates. - f(x) =(23) xf(x) =\left(\frac{2}{3}\right) ^{x}f(x) =(32​) x

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. - 3ln⁡(6x) =63 \ln ( 6 x ) = 63ln(6x) =6

Correct AnswerverifiedShow Answer

Graph the function. -Use the graph of log⁡2x\log _ { 2 } xlog2​x to obtain the graph of f(x) =1+log⁡2xf ( x ) = 1 + \log _ { 2 } xf(x) =1+log2​x .

Correct AnswerverifiedShow Answer

Graph the function. -Use the graph of f(x) =exf ( x ) = e ^ { x }f(x) =ex to obtain the graph of g(x) =ex−5g ( x ) = e ^ { x - 5 }g(x) =ex−5

Correct AnswerverifiedShow Answer

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - ex=3.9\mathrm { e } ^ { \mathrm { x } } = 3.9ex=3.9

Correct AnswerverifiedShow Answer

Rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm, and then round to three decimal places. - y=400(3.8) xy = 400 ( 3.8 ) ^ { x }y=400(3.8) x

Correct AnswerverifiedShow Answer

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - log⁡3135−log⁡35\log _ { 3 } 135 - \log _ { 3 } 5log3​135−log3​5

Correct AnswerverifiedShow Answer

Write the equation in its equivalent exponential form. - log⁡b8=3\log _ { b } 8 = 3logb​8=3

Correct AnswerverifiedShow Answer

Find the domain of the logarithmic function. - $f ( x ) = \log _ { 5 } ( x - 9 ) ^ { 2 }$

Correct Answer
verified

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. - $\log _ { 5 } \left( \frac { \sqrt { x } } { 125 } \right)$

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Evaluate or simplify the expression without using a calculator. - $10 \log 6$

Correct Answer
verified

Use Natural Logarithms Evaluate or simplify the expression without using a calculator. - $\ln \mathrm { e } ^ { 11 }$

Correct Answer
verified

Correct Answer
verified

Write the equation in its equivalent logarithmic form. - $13 ^ { x } = 169$

Correct Answer
verified

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $\mathrm { e } ^ { 5 \mathrm { x } - 8 } - 10 = 1178$

Correct Answer
verified

Correct Answer
verified

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $6 \log _ { b } q - \log _ { b } r$

Correct Answer
verified

Graph the function by making a table of coordinates. - $f(x) =\left(\frac{2}{3}\right) ^{x}$ $Graph the function by making a table of coordinates. - f(x) =\left(\frac{2}{3}\right) ^{x} A) B) C) D)$

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. - $3 \ln ( 6 x ) = 6$

Correct Answer
verified

Graph the function. -Use the graph of $\log _ { 2 } x$ to obtain the graph of $f ( x ) = 1 + \log _ { 2 } x$ . $Graph the function. -Use the graph of \log _ { 2 } x to obtain the graph of f ( x ) = 1 + \log _ { 2 } x . A) B) C) D)$

Correct Answer
verified

Graph the function. -Use the graph of $f ( x ) = e ^ { x }$ to obtain the graph of $g ( x ) = e ^ { x - 5 }$ $Graph the function. -Use the graph of f ( x ) = e ^ { x } to obtain the graph of g ( x ) = e ^ { x - 5 } A) B) C) D)$

Correct Answer
verified

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $\mathrm { e } ^ { \mathrm { x } } = 3.9$

Correct Answer
verified

Rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm, and then round to three decimal places. - $y = 400 ( 3.8 ) ^ { x }$

Correct Answer
verified

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $\log _ { 3 } 135 - \log _ { 3 } 5$

Correct Answer
verified

Write the equation in its equivalent exponential form. - $\log _ { b } 8 = 3$

Correct Answer
verified