Question 1

Solve the equation.
- 3−x=193 ^ { - x } = \frac { 1 } { 9 }3−x=91​

Accepted Answer

A)    {−2}\{ - 2 \}{−2} 
B)    {12}\left\{ \frac { 1 } { 2 } \right\}{21​} 
C)    {13}\left\{ \frac { 1 } { 3 } \right\}{31​} 
D)    {2}\{ 2 \}{2}E) A) and B)
F) A) and C)

Question 2

Choose the one alternative that best completes the statement or answers the question.
Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the
solution.
- 46x=4.84 ^ { 6 x } = 4.846x=4.8

Accepted Answer

A)   {0.19}
B)   {6.79}
C)   {0.22}
D)   {6.20} E) A) and B)
F) A) and C)

Question 3

Solve the equation.
- log⁡5x=2\log _ { 5 } x = 2log5​x=2

Accepted Answer

A)   {7}
B)   {25}
C)   {32}
D)   {10} E) C) and D)
F) A) and D)

Question 4

Accepted Answer

Graph the function.- f(x) =e−xf ( x )  = e ^ { - x }f(x) =e−x  
A)  
B)   
C)  
D)   E) B) and D)
F) undefined

Question 5

Accepted Answer

Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function.- f(x) =2−x+5\begin{array} { l } f ( x )  = 2 ^ { - x } + 5 \\end{array}f(x) =2−x+5​  
A)   domain of  f:(−∞,∞) f : ( - \infty , \infty ) f:(−∞,∞)  ; range of  f:(2,∞) f : ( 2 , \infty ) f:(2,∞)   horizontal asymptote:  y=2\mathrm { y } = 2y=2 
B)   domain of  f:(−∞,∞) f : ( - \infty , \infty ) f:(−∞,∞)  ; range of  f:(5,∞) f : ( 5 , \infty ) f:(5,∞)   horizontal asymptote:  y=5\mathrm { y } = 5y=5  
C)   domain of  f:(−∞,∞) f : ( - \infty , \infty ) f:(−∞,∞)  ; range of  f:(2,∞) f : ( 2 , \infty ) f:(2,∞)  horizontal asymptote:  y=2\mathrm { y } = 2y=2 
D)   domain of  f:(−∞,∞) f : ( - \infty , \infty ) f:(−∞,∞)  ; range of  f:(5,∞) f : ( 5 , \infty ) f:(5,∞)    horizontal asymptote:  y=5\mathrm { y } = 5y=5  E) B) and D)
F) undefined

Question 6

Accepted Answer

Use transformations to graph the function.-  Use the graph of log⁡4x to obtain the graph of f(x) =log⁡4(x−1) . 	ext { Use the graph of } \log _ { 4 } x 	ext { to obtain the graph of } f ( x )  = \log _ { 4 } ( x - 1 )  	ext {. } Use the graph of log4​x to obtain the graph of f(x) =log4​(x−1) .   
A)  
B)  
C)  
D)   E) C) and D)
F) B) and D)

Question 7

Accepted Answer

Graph the function.- y=log⁡1/4xy=\log _{1 / 4} xy=log1/4​x  
A)  
B)  
C)  
D)   E) B) and C)
F) B) and D)

Question 8

Find the value of the expression.
-Let  log⁡bA=5\log _ { b } A = 5logb​A=5  and  log⁡bB=−4\log _ { b } B = - 4logb​B=−4 . Find  log⁡bB2\log _ { b } B ^ { 2 }logb​B2 .

Accepted Answer

A)    −8- 8−8 В)   −16- 16−16 
C)   16
D)   10 E) A) and C)
F) C) and D)

Question 9

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
-The profit P for selling x items is given by the equation P(x) = 2x - 500. Express the sales amount x as a function
of the profit P.

Accepted Answer

The answer of Write the word or phrase that best...

Question 10

Solve the problem. Round your answer to three decimals.
-How long will it take for an investment to triple in value if it earns 8.5% compounded continuously?

Accepted Answer

A)   12.925 years
B)   8.155 years
C)   6.462 years
D)   13.797 yearsE) B) and D)
F) B) and C)

Question 11

Solve the problem.
-The logistic growth functi  f(t) =8001+9.0e−0.16tf ( t )  = \frac { 800 } { 1 + 9.0 e ^ { - 0.16 t } }f(t) =1+9.0e−0.16t800​  describes the population of a species of butterflies t months after they are introduced to a non-threatening habitat. How many butterflies are expected in the habitat after 15
Months?

Accepted Answer

A)   801 butterflies
B)   1,200 butterflies
C)   440 butterflies
D)   12,000 butterflies E) A) and B)
F) All of the above

Question 12

Find the inverse of the function and state its domain and range .
- {(−3,4) ,(−1,5) ,(0,2) ,(2,6) ,(5,7) }\{ ( - 3,4 )  , ( - 1,5 )  , ( 0,2 )  , ( 2,6 )  , ( 5,7 )  \}{(−3,4) ,(−1,5) ,(0,2) ,(2,6) ,(5,7) }

Accepted Answer

A)    {(3,4) ,(1,5) ,(0,2) ,(−2,6) ,(−5,7) };D={3,1,0,−2,−5};R={2,4,5,6,7}\{ ( 3,4 )  , ( 1,5 )  , ( 0,2 )  , ( - 2,6 )  , ( - 5,7 )  \} ; \mathrm { D } = \{ 3,1,0 , - 2 , - 5 \} ; \mathrm { R } = \{ 2,4,5,6,7 \}{(3,4) ,(1,5) ,(0,2) ,(−2,6) ,(−5,7) };D={3,1,0,−2,−5};R={2,4,5,6,7} 
B)    {(3,−4) ,(1,−5) ,(0,−2) ,(−2,−6) ,(−5,−7) };D={3,1,0,−2,−5};R={−7,−6,−5,−4,−2}\{ ( 3 , - 4 )  , ( 1 , - 5 )  , ( 0 , - 2 )  , ( - 2 , - 6 )  , ( - 5 , - 7 )  \} ; \mathrm { D } = \{ 3,1,0 , - 2 , - 5 \} ; \mathrm { R } = \{ - 7 , - 6 , - 5 , - 4 , - 2 \}{(3,−4) ,(1,−5) ,(0,−2) ,(−2,−6) ,(−5,−7) };D={3,1,0,−2,−5};R={−7,−6,−5,−4,−2} 
C)    {(4,−3) ,(5,−1) ,(2,0) ,(6,2) ,(7,5) }D={2,4,5,6,7};R={−3,−1,0,2,5}\{ ( 4 , - 3 )  , ( 5 , - 1 )  , ( 2,0 )  , ( 6,2 )  , ( 7,5 )  \} \mathrm { D } = \{ 2,4,5,6,7 \} ; \mathrm { R } = \{ - 3 , - 1,0,2,5 \}{(4,−3) ,(5,−1) ,(2,0) ,(6,2) ,(7,5) }D={2,4,5,6,7};R={−3,−1,0,2,5} 
D)    {(−3,−4) ,(−1,−5) ,(0,−2) ,(2,−6) ,(5,−7) };D={−3,−1,0,2,5};R={−7,−6,−5,−4,−2}\{ ( - 3 , - 4 )  , ( - 1 , - 5 )  , ( 0 , - 2 )  , ( 2 , - 6 )  , ( 5 , - 7 )  \} ; \mathrm { D } = \{ - 3 , - 1,0,2,5 \} ; \mathrm { R } = \{ - 7 , - 6 , - 5 , - 4 , - 2 \}{(−3,−4) ,(−1,−5) ,(0,−2) ,(2,−6) ,(5,−7) };D={−3,−1,0,2,5};R={−7,−6,−5,−4,−2}E) A) and B)
F) B) and C)

Question 13

Write as the sum and/or difference of logarithms. Express powers as factors.
- log⁡3(x2y6) \log _ { 3 } \left( \frac { x ^ { 2 } } { y ^ { 6 } } \right) log3​(y6x2​)

Accepted Answer

A)    6log⁡3y−2log⁡3x6 \log _ { 3 } y - 2 \log _ { 3 } x6log3​y−2log3​x 
B)    2log⁡3x+6log⁡3y2 \log _ { 3 } x + 6 \log _ { 3 } y2log3​x+6log3​y 
C)    13log⁡3(xy) \frac { 1 } { 3 } \log _ { 3 } \left( \frac { \mathrm { x } } { \mathrm { y } } \right) 31​log3​(yx​)  
D)    2log⁡3x−6log⁡3y2 \log _ { 3 } x - 6 \log _ { 3 } y2log3​x−6log3​yE) All of the above
F) B) and D)

Question 14

Change the logarithmic expression to an equivalent expression involving an exponent.
- log⁡5x=2\log _ { 5 } x = 2log5​x=2

Accepted Answer

A)    x2=5x ^ { 2 } = 5x2=5 
B)    5x=25 ^ { \mathrm { x } } = 25x=2 
C)    52=x5 ^ { 2 } = x52=x 
D)    25=x2 ^ { 5 } = x25=xE) B) and C)
F) None of the above

Question 15

Find the exact value of the logarithmic expression.
- log⁡101,000\log _ { 10 } 1,000log10​1,000

Accepted Answer

A)   30
B)    −3- 3−3 
C)    11000\frac { 1 } { 1000 }10001​ 
D)   3 E) B) and C)
F) A) and D)

Question 16

For the given functions f and g, find the requested composite function value.
- f(x) =13x2−4x,g(x) =16x−10;f ( x )  = 13 x ^ { 2 } - 4 x , \quad g ( x )  = 16 x - 10 ; \quadf(x) =13x2−4x,g(x) =16x−10;  Find  (f∘g) (9) ( f \circ g )  ( 9 ) (f∘g) (9)  .

Accepted Answer

A)   16,262
B)   136,278
C)   232,892
D)   216,630 E) C) and D)
F) B) and C)

Question 17

Accepted Answer

Use transformations to graph the function.-  Use the graph of log⁡4x to obtain the graph of f(x) =−1+log⁡4x. 	ext { Use the graph of } \log _ { 4 } x 	ext { to obtain the graph of } f ( x )  = - 1 + \log _ { 4 } x 	ext {. } Use the graph of log4​x to obtain the graph of f(x) =−1+log4​x.   
A)  
B)  
C)  
D)   E) B) and C)
F) All of the above

Question 18

Solve the problem.
-If $5,000 is invested for 6 years at 5%, compounded continuously, find the future value.

Accepted Answer

The answer of Solve the problem.
-If $5,000 is invested for...

Question 19

Write as the sum and/or difference of logarithms. Express powers as factors.
-  2">ln⁡((x+5) (x−2) (x−8) 4) 4/3,x>2\ln \left( \frac { ( x + 5 )  ( x - 2 )  } { ( x - 8 )  ^ { 4 } } \right)  ^ { 4 / 3 } , \quad x > 2ln((x−8) 4(x+5) (x−2) ​) 4/3,x>2

Accepted Answer

A)    4ln⁡(x+5) −3ln⁡(x−2) −163ln⁡(x−8) 4 \ln ( x + 5 )  - 3 \ln ( x - 2 )  - \frac { 16 } { 3 } \ln ( x - 8 ) 4ln(x+5) −3ln(x−2) −316​ln(x−8)  
B)    43ln⁡(x2+7x−10) −163ln⁡(x−8) \frac { 4 } { 3 } \ln \left( x ^ { 2 } + 7 x - 10 \right)  - \frac { 16 } { 3 } \ln ( x - 8 ) 34​ln(x2+7x−10) −316​ln(x−8)  
C)    ln⁡(x+5) +ln⁡(x−2) +ln⁡4−16ln⁡(x−8) −ln⁡3\ln ( x + 5 )  + \ln ( x - 2 )  + \ln 4 - 16 \ln ( x - 8 )  - \ln 3ln(x+5) +ln(x−2) +ln4−16ln(x−8) −ln3 
D)    43ln⁡(x+5) +43ln⁡(x−2) −163ln⁡(x−8) \frac { 4 } { 3 } \ln ( x + 5 )  + \frac { 4 } { 3 } \ln ( x - 2 )  - \frac { 16 } { 3 } \ln ( x - 8 ) 34​ln(x+5) +34​ln(x−2) −316​ln(x−8) E) C) and D)
F) B) and C)

Question 20

Solve the problem.
-Which of the two rates would yield the larger amount in 1 year: 5.2% compounded monthly or 5.1% compounded daily?

Accepted Answer

A)   5.2% compounded monthly
B)   5.1% compounded daily
C)   They will yield the same amount.D) A) and B)
E) A) and C)

Exam 4: Exponential and Logarithmic Functions

Correct Answer
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Find the value of the expression. -Let $\log _ { b } A = 5$ and $\log _ { b } B = - 4$ . Find $\log _ { b } B ^ { 2 }$ .

Correct Answer
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Write as the sum and/or difference of logarithms. Express powers as factors. - $\log _ { 3 } \left( \frac { x ^ { 2 } } { y ^ { 6 } } \right)$

Correct Answer
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Write as the sum and/or difference of logarithms. Express powers as factors. - $\ln \left( \frac { ( x + 5 ) ( x - 2 ) } { ( x - 8 ) ^ { 4 } } \right) ^ { 4 / 3 } , \quad x > 2$

Correct Answer
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Write the word or phrase that best completes each statement or answers the question. Solve the problem. -The profit P for selling x items is given by the equation P(x) = 2x - 500. Express the sales amount x as a function of the profit P.

Correct Answer
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Solve the problem. -If $5,000 is invested for 6 years at 5%, compounded continuously, find the future value.

Correct Answer
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Solve the problem. Round your answer to three decimals. -How long will it take for an investment to triple in value if it earns 8.5% compounded continuously?

Correct Answer
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Correct Answer
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Correct Answer
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Solve the equation. - $3 ^ { - x } = \frac { 1 } { 9 }$

Correct Answer
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Solve the equation. - $\log _ { 5 } x = 2$

Correct Answer
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Change the logarithmic expression to an equivalent expression involving an exponent. - $\log _ { 5 } x = 2$

Correct Answer
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Find the exact value of the logarithmic expression. - $\log _ { 10 } 1,000$

Correct Answer
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Choose the one alternative that best completes the statement or answers the question. Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $4 ^ { 6 x } = 4.8$

Correct Answer
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For the given functions f and g, find the requested composite function value. - $f ( x ) = 13 x ^ { 2 } - 4 x , \quad g ( x ) = 16 x - 10 ; \quad$ Find $( f \circ g ) ( 9 )$ .

Correct Answer
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Correct Answer
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Solve the problem. -Which of the two rates would yield the larger amount in 1 year: 5.2% compounded monthly or 5.1% compounded daily?

Correct Answer
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Find the inverse of the function and state its domain and range . - $\{ ( - 3,4 ) , ( - 1,5 ) , ( 0,2 ) , ( 2,6 ) , ( 5,7 ) \}$

Correct Answer
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Solve the problem. -The logistic growth functi $f ( t ) = \frac { 800 } { 1 + 9.0 e ^ { - 0.16 t } }$ describes the population of a species of butterflies t months after they are introduced to a non-threatening habitat. How many butterflies are expected in the habitat after 15 Months?

Correct Answer
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Correct Answer
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Exam 4: Exponential and Logarithmic Functions

Correct AnswerverifiedShow Answer

Find the value of the expression. -Let log⁡bA=5\log _ { b } A = 5logb​A=5 and log⁡bB=−4\log _ { b } B = - 4logb​B=−4 . Find log⁡bB2\log _ { b } B ^ { 2 }logb​B2 .

Correct AnswerverifiedShow Answer

Write as the sum and/or difference of logarithms. Express powers as factors. - log⁡3(x2y6) \log _ { 3 } \left( \frac { x ^ { 2 } } { y ^ { 6 } } \right) log3​(y6x2​)

Correct AnswerverifiedShow Answer

Write as the sum and/or difference of logarithms. Express powers as factors. - ln⁡((x+5) (x−2) (x−8) 4) 4/3,x>2\ln \left( \frac { ( x + 5 ) ( x - 2 ) } { ( x - 8 ) ^ { 4 } } \right) ^ { 4 / 3 } , \quad x > 2ln((x−8) 4(x+5) (x−2) ​) 4/3,x>2

Correct AnswerverifiedShow Answer

Write the word or phrase that best completes each statement or answers the question. Solve the problem. -The profit P for selling x items is given by the equation P(x) = 2x - 500. Express the sales amount x as a function of the profit P.

Correct AnswerverifiedShow Answer

Solve the problem. -If $5,000 is invested for 6 years at 5%, compounded continuously, find the future value.

Correct AnswerverifiedShow Answer

Solve the problem. Round your answer to three decimals. -How long will it take for an investment to triple in value if it earns 8.5% compounded continuously?

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Solve the equation. - 3−x=193 ^ { - x } = \frac { 1 } { 9 }3−x=91​

Correct AnswerverifiedShow Answer

Solve the equation. - log⁡5x=2\log _ { 5 } x = 2log5​x=2

Correct AnswerverifiedShow Answer

Change the logarithmic expression to an equivalent expression involving an exponent. - log⁡5x=2\log _ { 5 } x = 2log5​x=2

Correct AnswerverifiedShow Answer

Find the exact value of the logarithmic expression. - log⁡101,000\log _ { 10 } 1,000log10​1,000

Correct AnswerverifiedShow Answer

Choose the one alternative that best completes the statement or answers the question. Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - 46x=4.84 ^ { 6 x } = 4.846x=4.8

Correct AnswerverifiedShow Answer

For the given functions f and g, find the requested composite function value. - f(x) =13x2−4x,g(x) =16x−10;f ( x ) = 13 x ^ { 2 } - 4 x , \quad g ( x ) = 16 x - 10 ; \quadf(x) =13x2−4x,g(x) =16x−10; Find (f∘g) (9) ( f \circ g ) ( 9 ) (f∘g) (9) .

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Solve the problem. -Which of the two rates would yield the larger amount in 1 year: 5.2% compounded monthly or 5.1% compounded daily?

Correct AnswerverifiedShow Answer

Find the inverse of the function and state its domain and range . - {(−3,4) ,(−1,5) ,(0,2) ,(2,6) ,(5,7) }\{ ( - 3,4 ) , ( - 1,5 ) , ( 0,2 ) , ( 2,6 ) , ( 5,7 ) \}{(−3,4) ,(−1,5) ,(0,2) ,(2,6) ,(5,7) }

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct Answer
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Find the value of the expression. -Let $\log _ { b } A = 5$ and $\log _ { b } B = - 4$ . Find $\log _ { b } B ^ { 2 }$ .

Correct Answer
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Write as the sum and/or difference of logarithms. Express powers as factors. - $\log _ { 3 } \left( \frac { x ^ { 2 } } { y ^ { 6 } } \right)$

Correct Answer
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Write as the sum and/or difference of logarithms. Express powers as factors. - $\ln \left( \frac { ( x + 5 ) ( x - 2 ) } { ( x - 8 ) ^ { 4 } } \right) ^ { 4 / 3 } , \quad x > 2$

Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Solve the equation. - $3 ^ { - x } = \frac { 1 } { 9 }$

Correct Answer
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Solve the equation. - $\log _ { 5 } x = 2$

Correct Answer
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Change the logarithmic expression to an equivalent expression involving an exponent. - $\log _ { 5 } x = 2$

Correct Answer
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Find the exact value of the logarithmic expression. - $\log _ { 10 } 1,000$

Correct Answer
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Choose the one alternative that best completes the statement or answers the question. Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $4 ^ { 6 x } = 4.8$

Correct Answer
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For the given functions f and g, find the requested composite function value. - $f ( x ) = 13 x ^ { 2 } - 4 x , \quad g ( x ) = 16 x - 10 ; \quad$ Find $( f \circ g ) ( 9 )$ .

Correct Answer
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Correct Answer
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Correct Answer
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Find the inverse of the function and state its domain and range . - $\{ ( - 3,4 ) , ( - 1,5 ) , ( 0,2 ) , ( 2,6 ) , ( 5,7 ) \}$

Correct Answer
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Correct Answer
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Correct Answer
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