Question 1

Solve the equation.
-$\log _ { 3 } x = 4$

Accepted Answer

A)  $\{ 64 \}$ 
B)  $\{ 12 \}$ 
C)  $\{ 1.26 \}$ 
D)  $\{ 81 \}$ 
A)  $\{ 64 \}$ 
B)  $\{ 12 \}$ 
C)  $\{ 1.26 \}$ 
D)  $\{ 81 \}$

Question 2

Write the word or phrase that best completes each statement or answers the question.
-The half-life of radium is 1690 years. If 150 grams is present now, how long (to the nearest year) till only 100
grams are present?

Accepted Answer

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

Question 3

Choose the one alternative that best completes the statement or answers the question.
-After introducing an inhibitor into a culture of luminescent bacteria, a scientist monitors the luminosity produced by the culture. Use a graphing utility to fit a logarithmic function to the data. Predict the luminosity after 20 hours.
$\begin{array}{l|ccccccc}
\text { Time, hrs } & 2 & 3 & 4 & 5 & 8 & 10 & 15 \
\hline \text { Luminosity } & 77.4 & 60.8 & 54.5 & 45.8 & 30.0 & 24.3 & 10.5
\end{array}$

Accepted Answer

A)  $y = 98.75 - 32.66 \ln ( \mathrm { x } ) , 0.91$ 
B)  $y = 107.55 - 41 \ln ( x ) , - 15.27$ 
C)  $\mathrm { y } = 112.97 - 45.97 \ln ( \mathrm { x } ) , - 24.74$ 
D)  $y = 100.5 - 32.7 \ln ( x ) , 2.54$ 
A)  $y = 98.75 - 32.66 \ln ( \mathrm { x } ) , 0.91$ 
B)  $y = 107.55 - 41 \ln ( x ) , - 15.27$ 
C)  $\mathrm { y } = 112.97 - 45.97 \ln ( \mathrm { x } ) , - 24.74$ 
D)  $y = 100.5 - 32.7 \ln ( x ) , 2.54$

Question 4

Change the logarithmic expression to an equivalent expression involving an exponent.
-$\log _ { 2 } 8 = 3$

Accepted Answer

A)  $2 ^ { 8 } = 3$ 
B)  $2 ^ { 3 } = 8$ 
C)  $8 ^ { 3 } = 2$ 
D)  $3 ^ { 2 } = 8$ 
A)  $2 ^ { 8 } = 3$ 
B)  $2 ^ { 3 } = 8$ 
C)  $8 ^ { 3 } = 2$ 
D)  $3 ^ { 2 } = 8$

Question 5

For the given functions f and g, find the requested composite function.
-$f ( x ) = x ^ { 2 } - 5 , \quad g ( x ) = x ^ { 2 } - 8 ; \quad$ Find $( f \circ g ) ( x )$

Accepted Answer

A)  $x ^ { 4 } - 16 x ^ { 2 } + 59$ 
B)  $x ^ { 4 } + 17$ 
C)  $x ^ { 4 } + 59$ 
D)  $x ^ { 4 } - 10 x ^ { 2 } + 17$ 
A)  $x ^ { 4 } - 16 x ^ { 2 } + 59$ 
B)  $x ^ { 4 } + 17$ 
C)  $x ^ { 4 } + 59$ 
D)  $x ^ { 4 } - 10 x ^ { 2 } + 17$

Question 6

Write the word or phrase that best completes each statement or answers the question.
-A culture of bacteria obeys the law of uninhibited growth. If 140,000 bacteria are present initially and there are
609,000 after 6 hours, how long will it take for the population to reach one million?

Accepted Answer

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

Question 7

Find the domain of the function.
-$$f ( x ) = \log _ { 4 } ( x - 9 ) ^ { 2 }$$

Accepted Answer

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

Question 8

Write the word or phrase that best completes each statement or answers the question.
-The rates of death (in number of deaths per 100,000 population) for 1-4 year olds in the United States between 1980-1995 are given below. (Source: NCHS Data Warehouse)
$\begin{array}{c|c}
\text { Year } & \text { Rate of Death } \
\hline 1980 & 91.4 \
\hline 1985 & 74.5 \
\hline 1990 & 69.3 \
\hline 1995 & 61.3
\end{array}$ A logarithmic equation that models this data is $y = 822.99 - 167.55 \ln x$ where $x$ represents the number of years since 1900 . Use this equation to predict the rate of death for 1-4 year olds in 2005 .

Accepted Answer

43.2 death

Question 9

Choose the one alternative that best completes the statement or answers the question.
The graph of a logarithmic function is shown. Select the function which matches the graph.
-

Accepted Answer

A)  $y = \log ( x - 1 )$ 
B)  $y = \log ( x ) - 1$ 
C)  $y = \log ( 1 - x )$ 
D)  $y = 1 - \log ( x )$ 
A)  $y = \log ( x - 1 )$ 
B)  $y = \log ( x ) - 1$ 
C)  $y = \log ( 1 - x )$ 
D)  $y = 1 - \log ( x )$

Question 10

Solve the equation.
-$$23 ^ { x } = 1$$

Accepted Answer

A)  $\{ 0 \}$ 
B)  $\left\{ \frac { 1 } { 23 } \right\}$ 
C)  $\{ 1 \}$ 
D)  $\varnothing$ 
A)  $\{ 0 \}$ 
B)  $\left\{ \frac { 1 } { 23 } \right\}$ 
C)  $\{ 1 \}$ 
D)  $\varnothing$

Question 11

Solve the equation.
-$\log _ { 4 } ( x + 5 ) + \log _ { 4 } ( x - 1 ) = 2$

Accepted Answer

A)  $\{ - 7 \}$ 
B)  $\{ 3 , - 7 \}$ 
C)  $\{ 3 \}$ 
D)  $\{ 4 \}$ 
A)  $\{ - 7 \}$ 
B)  $\{ 3 , - 7 \}$ 
C)  $\{ 3 \}$ 
D)  $\{ 4 \}$

Question 12

Choose the one alternative that best completes the statement or answers the question.
Indicate whether the function is one-to-one.
-$$\{ ( 3 , - 12 ) , ( 7,4 ) , ( 12 , - 8 ) \}$$

Accepted Answer

A)  Yes 
B)  $\mathrm { No }$ 
A)  Yes 
B)  $\mathrm { No }$

Question 13

Write the word or phrase that best completes each statement or answers the question.
-$$\log _ { a } ( x - 7 ) - \log _ { a } ( x - 2 ) = \log _ { a } ( x - 4 ) - \log _ { a } ( x + 12 )$$

Accepted Answer

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

Question 14

Find the inverse function of f. State the domain and range of f.
-$$f ( x ) = \frac { 3 x - 2 } { x + 5 }$$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } + 5 } { 3 \mathrm { x } - 2 }$; domain of $\mathrm { f } : \{ \mathrm { x } \mid \mathrm { x } z - 5 \}$; range of $\mathrm { f } : \left\{ \mathrm { y } \mid \mathrm { y } \neq \frac { 2 } { 3 } \right\}$ 
B)  $f ^ { - 1 } ( x ) = \frac { 5 x + 2 } { 3 + x }$; domain of $f : \{ x \mid x \neq - 5 \}$; range of $f : \{ y \mid y \neq - 3 \}$ 
C)  $f ^ { - 1 } ( x ) = \frac { 3 x + 2 } { x - 5 }$; domain of $f : \{ x \mid x \neq - 5 \}$; range of $f : \{ y \mid y \neq 5 \}$ 
D)  $f ^ { - 1 } ( x ) = \frac { 5 x + 2 } { 3 - x }$; domain of $f : \{ x \mid x \neq - 5 \}$; range of $f : \{ y \mid y \neq 3 \}$ 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } + 5 } { 3 \mathrm { x } - 2 }$; domain of $\mathrm { f } : \{ \mathrm { x } \mid \mathrm { x } z - 5 \}$; range of $\mathrm { f } : \left\{ \mathrm { y } \mid \mathrm { y } \neq \frac { 2 } { 3 } \right\}$ 
B)  $f ^ { - 1 } ( x ) = \frac { 5 x + 2 } { 3 + x }$; domain of $f : \{ x \mid x \neq - 5 \}$; range of $f : \{ y \mid y \neq - 3 \}$ 
C)  $f ^ { - 1 } ( x ) = \frac { 3 x + 2 } { x - 5 }$; domain of $f : \{ x \mid x \neq - 5 \}$; range of $f : \{ y \mid y \neq 5 \}$ 
D)  $f ^ { - 1 } ( x ) = \frac { 5 x + 2 } { 3 - x }$; domain of $f : \{ x \mid x \neq - 5 \}$; range of $f : \{ y \mid y \neq 3 \}$

Question 15

Solve the problem.
-The formula $\mathrm { A } = 180 \mathrm { e } ^ { 0.036 \mathrm { t } }$ models the population of a particular city, in thousands, $\mathrm { t }$ years after 1998 . When will the population of the city reach 287 thousand?

Accepted Answer

A)  2011 
B)  2012 
C)  2014 
D)  2013 
A)  2011 
B)  2012 
C)  2014 
D)  2013

Question 16

Write the word or phrase that best completes each statement or answers the question.
-$$\text { If } f ( x ) = \frac { 1 } { 2 } x ^ { 2 } + 4 \text { and } g ( x ) = 2 x - a \text {, find a so that the graph of } f \circ g \text { crosses the } y \text {-axis at } 36$$

Accepted Answer

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

Question 17

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places.
-$\log _ { 6.9 } 2.8$

Accepted Answer

A)  $0.41$ 
B)  $0.53$ 
C)  $0.45$ 
D)  $1.88$ 
A)  $0.41$ 
B)  $0.53$ 
C)  $0.45$ 
D)  $1.88$

Question 18

Find the inverse. Determine whether the inverse represents a function.
-$\{ ( 6,5 ) , ( - 1,6 ) , ( - 3,7 ) , ( - 5,8 ) \}$

Accepted Answer

A)  $\{ ( 3,6 ) , ( 4,10 ) , ( 5,8 ) , ( 6,6 ) \}$; not a function 
B)  $\{ ( 4,3 ) , ( 3,8 ) , ( 6,10 ) , ( 4,5 ) \} ;$ not a function 
C)  $\{ ( 4,3 ) , ( 6,8 ) , ( 6,8 ) , ( 4,5 ) \} ;$ a function 
D)  $\{ ( 3,6 ) , ( 4,10 ) , ( 5,8 ) , ( 6,6 ) \} ;$ a function 
A)  $\{ ( 3,6 ) , ( 4,10 ) , ( 5,8 ) , ( 6,6 ) \}$; not a function 
B)  $\{ ( 4,3 ) , ( 3,8 ) , ( 6,10 ) , ( 4,5 ) \} ;$ not a function 
C)  $\{ ( 4,3 ) , ( 6,8 ) , ( 6,8 ) , ( 4,5 ) \} ;$ a function 
D)  $\{ ( 3,6 ) , ( 4,10 ) , ( 5,8 ) , ( 6,6 ) \} ;$ a function

Question 19

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator.
-$\log _ { 5 } 5 ^ { 4.71 }$

Accepted Answer

A)  $4.71$ 
B)  476 
C)  $0.212$ 
D)  5 
A)  $4.71$ 
B)  476 
C)  $0.212$ 
D)  5

Question 20

Graph the function.
-$f(x)=2-\ln (x+4)$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Solve the equation. - $\log _ { 3 } x = 4$

Write the word or phrase that best completes each statement or answers the question. -The half-life of radium is 1690 years. If 150 grams is present now, how long (to the nearest year) till only 100 grams are present?

Change the logarithmic expression to an equivalent expression involving an exponent. - $\log _ { 2 } 8 = 3$

For the given functions f and g, find the requested composite function. - $f ( x ) = x ^ { 2 } - 5 , \quad g ( x ) = x ^ { 2 } - 8 ; \quad$ Find $( f \circ g ) ( x )$

Write the word or phrase that best completes each statement or answers the question. -A culture of bacteria obeys the law of uninhibited growth. If 140,000 bacteria are present initially and there are 609,000 after 6 hours, how long will it take for the population to reach one million?

Find the domain of the function. - $f ( x ) = \log _ { 4 } ( x - 9 ) ^ { 2 }$

Choose the one alternative that best completes the statement or answers the question. The graph of a logarithmic function is shown. Select the function which matches the graph. -

Solve the equation. - $23 ^ { x } = 1$

Solve the equation. - $\log _ { 4 } ( x + 5 ) + \log _ { 4 } ( x - 1 ) = 2$

Choose the one alternative that best completes the statement or answers the question. Indicate whether the function is one-to-one. - $\{ ( 3 , - 12 ) , ( 7,4 ) , ( 12 , - 8 ) \}$

Write the word or phrase that best completes each statement or answers the question. - $\log _ { a } ( x - 7 ) - \log _ { a } ( x - 2 ) = \log _ { a } ( x - 4 ) - \log _ { a } ( x + 12 )$

Find the inverse function of f. State the domain and range of f. - $f ( x ) = \frac { 3 x - 2 } { x + 5 }$

Solve the problem. -The formula $\mathrm { A } = 180 \mathrm { e } ^ { 0.036 \mathrm { t } }$ models the population of a particular city, in thousands, $\mathrm { t }$ years after 1998 . When will the population of the city reach 287 thousand?

Write the word or phrase that best completes each statement or answers the question. - $\text { If } f ( x ) = \frac { 1 } { 2 } x ^ { 2 } + 4 \text { and } g ( x ) = 2 x - a \text {, find a so that the graph of } f \circ g \text { crosses the } y \text {-axis at } 36$

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. - $\log _ { 6.9 } 2.8$

Find the inverse. Determine whether the inverse represents a function. - $\{ ( 6,5 ) , ( - 1,6 ) , ( - 3,7 ) , ( - 5,8 ) \}$

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - $\log _ { 5 } 5 ^ { 4.71 }$

Graph the function. - $f(x)=2-\ln (x+4)$ $Graph the function. - f(x)=2-\ln (x+4)$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 4: Exponential and Logarithmic Functions

Solve the equation. - log⁡3x=4\log _ { 3 } x = 4log3​x=4

Write the word or phrase that best completes each statement or answers the question. -The half-life of radium is 1690 years. If 150 grams is present now, how long (to the nearest year) till only 100 grams are present?

Change the logarithmic expression to an equivalent expression involving an exponent. - log⁡28=3\log _ { 2 } 8 = 3log2​8=3

For the given functions f and g, find the requested composite function. - f(x)=x2−5,g(x)=x2−8;f ( x ) = x ^ { 2 } - 5 , \quad g ( x ) = x ^ { 2 } - 8 ; \quadf(x)=x2−5,g(x)=x2−8; Find (f∘g)(x)( f \circ g ) ( x )(f∘g)(x)

Write the word or phrase that best completes each statement or answers the question. -A culture of bacteria obeys the law of uninhibited growth. If 140,000 bacteria are present initially and there are 609,000 after 6 hours, how long will it take for the population to reach one million?

Find the domain of the function. - f(x)=log⁡4(x−9)2f ( x ) = \log _ { 4 } ( x - 9 ) ^ { 2 }f(x)=log4​(x−9)2

Choose the one alternative that best completes the statement or answers the question. The graph of a logarithmic function is shown. Select the function which matches the graph. -

Solve the equation. - 23x=123 ^ { x } = 123x=1

Solve the equation. - log⁡4(x+5)+log⁡4(x−1)=2\log _ { 4 } ( x + 5 ) + \log _ { 4 } ( x - 1 ) = 2log4​(x+5)+log4​(x−1)=2

Choose the one alternative that best completes the statement or answers the question. Indicate whether the function is one-to-one. - {(3,−12),(7,4),(12,−8)}\{ ( 3 , - 12 ) , ( 7,4 ) , ( 12 , - 8 ) \}{(3,−12),(7,4),(12,−8)}

Find the inverse function of f. State the domain and range of f. - f(x)=3x−2x+5f ( x ) = \frac { 3 x - 2 } { x + 5 }f(x)=x+53x−2​

Solve the problem. -The formula A=180e0.036t\mathrm { A } = 180 \mathrm { e } ^ { 0.036 \mathrm { t } }A=180e0.036t models the population of a particular city, in thousands, t\mathrm { t }t years after 1998 . When will the population of the city reach 287 thousand?

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. - log⁡6.92.8\log _ { 6.9 } 2.8log6.9​2.8

Find the inverse. Determine whether the inverse represents a function. - {(6,5),(−1,6),(−3,7),(−5,8)}\{ ( 6,5 ) , ( - 1,6 ) , ( - 3,7 ) , ( - 5,8 ) \}{(6,5),(−1,6),(−3,7),(−5,8)}

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - log⁡554.71\log _ { 5 } 5 ^ { 4.71 }log5​54.71

Graph the function. - f(x)=2−ln⁡(x+4)f(x)=2-\ln (x+4)f(x)=2−ln(x+4)

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Solve the equation. - $\log _ { 3 } x = 4$

Change the logarithmic expression to an equivalent expression involving an exponent. - $\log _ { 2 } 8 = 3$

For the given functions f and g, find the requested composite function. - $f ( x ) = x ^ { 2 } - 5 , \quad g ( x ) = x ^ { 2 } - 8 ; \quad$ Find $( f \circ g ) ( x )$

Find the domain of the function. - $f ( x ) = \log _ { 4 } ( x - 9 ) ^ { 2 }$

Solve the equation. - $23 ^ { x } = 1$

Solve the equation. - $\log _ { 4 } ( x + 5 ) + \log _ { 4 } ( x - 1 ) = 2$

Choose the one alternative that best completes the statement or answers the question. Indicate whether the function is one-to-one. - $\{ ( 3 , - 12 ) , ( 7,4 ) , ( 12 , - 8 ) \}$

Find the inverse function of f. State the domain and range of f. - $f ( x ) = \frac { 3 x - 2 } { x + 5 }$

Solve the problem. -The formula $\mathrm { A } = 180 \mathrm { e } ^ { 0.036 \mathrm { t } }$ models the population of a particular city, in thousands, $\mathrm { t }$ years after 1998 . When will the population of the city reach 287 thousand?

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. - $\log _ { 6.9 } 2.8$

Find the inverse. Determine whether the inverse represents a function. - $\{ ( 6,5 ) , ( - 1,6 ) , ( - 3,7 ) , ( - 5,8 ) \}$

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - $\log _ { 5 } 5 ^ { 4.71 }$

Graph the function. - $f(x)=2-\ln (x+4)$ $Graph the function. - f(x)=2-\ln (x+4)$