Question 1

Evaluate the expression without using a calculator.
-$\log _ { 10 } 1000$

Accepted Answer

A)  3 
B)  30 
C)  $\frac { 1 } { 1000 }$ 
D)  $- 3$ 1000 
A)  3 
B)  30 
C)  $\frac { 1 } { 1000 }$ 
D)  $- 3$ 1000

Question 2

Model Exponential Growth and Decay
Solve.
-An endangered species of fish has a population that is decreasing exponentially $\left( A = A _ { 0 } e ^ { k t } \right)$. The population 9 years ago was 1500 . Today, only 1000 of the fish are alive. Once the population drops below 100 , the situation will be irreversible. When will this happen, according to the model? (Round to the nearest whole year.)

Accepted Answer

A)  51 years from today 
B)  52 years from today 
C)  50 years from today 
D)  53 years from today 
A)  51 years from today 
B)  52 years from today 
C)  50 years from today 
D)  53 years from today

Question 3

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.
-$$\log ( 4 + x ) - \log ( x - 2 ) = \log 3$$

Accepted Answer

A)  $\{ 5 \}$ 
B)  $\left\{ \frac { 1 } { 2 } \right\}$ 
C)  $\{ - 5 \}$ 
D)  $\varnothing$ 
A)  $\{ 5 \}$ 
B)  $\left\{ \frac { 1 } { 2 } \right\}$ 
C)  $\{ - 5 \}$ 
D)  $\varnothing$

Question 4

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.
-$$\ln 7 + \ln ( x - 1 ) = 0$$

Accepted Answer

A)  $\left\{ \frac { 8 } { 7 } \right\}$ 
B)  $\left\{ \frac { 7 } { 8 } \right\}$ 
C)  $\{ 1 \}$ 
D)  $\left\{ \frac { 1 } { 7 } \right\}$ 
A)  $\left\{ \frac { 8 } { 7 } \right\}$ 
B)  $\left\{ \frac { 7 } { 8 } \right\}$ 
C)  $\{ 1 \}$ 
D)  $\left\{ \frac { 1 } { 7 } \right\}$

Question 5

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

Accepted Answer

A)  $1 - \log _ { 5 } x$ 
B)  5 
C)  $\frac { 1 } { x }$ 
D)  $- \log _ { 5 } x$ 
A)  $1 - \log _ { 5 } x$ 
B)  5 
C)  $\frac { 1 } { x }$ 
D)  $- \log _ { 5 } x$

Question 6

Graph the function.
-$$\text { Use the graph of } f ( x ) = e ^ { x } \text { to obtain the graph of } g ( x ) = \frac { 1 } { 3 } e ^ { x } \text {. }$$

Accepted Answer

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

Question 7

Graph the function.
-Use the graph of $f ( x ) = \log x$ to obtain the graph of $g ( x ) = 5 - \log x$.

Accepted Answer

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

Question 8

Solve the exponential equation. Express the solution set in terms of natural logarithms.
-$$\mathrm { e } ^ { 5 \mathrm { x } } = 8$$

Accepted Answer

A)  $\left\{ \frac { \ln 8 } { 5 } \right\}$ 
B)  $\left\{ \frac { \ln 5 } { 8 } \right\}$ 
C)  $\left\{ \frac { 8 } { 5 } \mathrm { e } \right\}$ 
D)  $\{ 5 \ln 8 \}$ 
A)  $\left\{ \frac { \ln 8 } { 5 } \right\}$ 
B)  $\left\{ \frac { \ln 5 } { 8 } \right\}$ 
C)  $\left\{ \frac { 8 } { 5 } \mathrm { e } \right\}$ 
D)  $\{ 5 \ln 8 \}$

Question 9

Solve the equation by expressing each side as a power of the same base and then equating exponents.
-$$\mathrm { e } ^ { \mathrm { x } + 5 } = \frac { 1 } { \mathrm { e } ^ { 10 } }$$

Accepted Answer

A)  $\{ - 15 \}$ 
B)  $\{ 15 \}$ 
C)  $\{ - 5 \}$ 
D)  $\{ 5 \}$ 
A)  $\{ - 15 \}$ 
B)  $\{ 15 \}$ 
C)  $\{ - 5 \}$ 
D)  $\{ 5 \}$

Question 10

Evaluate the expression without using a calculator.
-$\log _ { 3 } 81$

Accepted Answer

A)  4 
B)  81 
C)  12 
D)  3 
A)  4 
B)  81 
C)  12 
D)  3

Question 11

Solve the problem.
-The logistic growth function $f ( t ) = \frac { 800 } { 1 + 10.4 e ^ { - 0.2 t } }$ 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 13 months?

Accepted Answer

A)  451 butterflies 
B)  910 butterflies 
C)  801 butterflies 
D)  10,400 butterflies 
A)  451 butterflies 
B)  910 butterflies 
C)  801 butterflies 
D)  10,400 butterflies

Question 12

Graph the function.
-Use the graph of $f ( x ) = 2 ^ { x }$ to obtain the graph of $g ( x ) = 2 ^ { x + 2 } + 1$

Accepted Answer

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

Question 13

Solve the problem.
-The population in a particular country is growing at the rate of $1.3 \%$ per year. If $7,638,000$ people lived there in 1999 , how many will there be in the year 2004 ? Use $\mathrm { y } = \mathrm { y } _ { 0 } \mathrm { e } ^ { 0.013 \mathrm { t } }$ and round to the nearest ten-thousand.

Accepted Answer

A)  $8,150,000$ 
B)  $8,970,000$ 
C)  $7,990,000$ 
D)  $9,780,000$ 
A)  $8,150,000$ 
B)  $8,970,000$ 
C)  $7,990,000$ 
D)  $9,780,000$

Question 14

The graph of an exponential function is given. Select the function for the graph from the functions listed.
-

Accepted Answer

A)  $f ( x ) = 3 ^ { - x }$ 
B)  $f ( x ) = 3 ^ { x }$ 
C)  $f ( x ) = - 3 ^ { x }$ 
D)  $f ( x ) = - 3 ^ { - x }$ 
A)  $f ( x ) = 3 ^ { - x }$ 
B)  $f ( x ) = 3 ^ { x }$ 
C)  $f ( x ) = - 3 ^ { x }$ 
D)  $f ( x ) = - 3 ^ { - x }$

Question 15

Solve the problem.
-The size of the beaver population at a national park increases at the rate of $4.7 \%$ per year. If the size of the current population is 131 , find how many beavers there should be in 3 years. Use $\mathrm { y } = \mathrm { y } _ { \mathrm { o } } \mathrm { e } ^ { 0.047 \mathrm { t } }$ and round to the nearest whole number.

Accepted Answer

A)  151 
B)  153 
C)  149 
D)  155 
A)  151 
B)  153 
C)  149 
D)  155

Question 16

Graph the function.
-$f(x)=\left(\frac{1}{4}\right)^{x} \text { and } g(x)=\log 1 / 4 x$

Accepted Answer

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

Question 17

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.
-$\log _ { 9 } 7 + \log _ { 9 } x = 1$

Accepted Answer

A)  $\left\{ \frac { 9 } { 7 } \right\}$ 
B)  $\left\{ \frac { 7 } { 9 } \right\}$ 
C)  $\{ \sqrt [ 7 ] { 9 } \}$ 
D)  $\left\{ \frac { 1 } { 7 } \right\}$ 
A)  $\left\{ \frac { 9 } { 7 } \right\}$ 
B)  $\left\{ \frac { 7 } { 9 } \right\}$ 
C)  $\{ \sqrt [ 7 ] { 9 } \}$ 
D)  $\left\{ \frac { 1 } { 7 } \right\}$

Question 18

Graph the function.
-Use the graph of $\log _ { 5 } x$ to obtain the graph of $f ( x ) = 2 \log _ { 5 } x$.

Accepted Answer

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

Question 19

The graph of a logarithmic function is given. Select the function for the graph from the options.
-

Accepted Answer

A)  $f ( x ) = \log _ { 4 } ( x - 1 )$ 
B)  $f ( x ) = \log _ { 4 } x$ 
C)  $f ( x ) = \log _ { 4 } ( x + 1 )$ 
D)  $f ( x ) = \log _ { 4 } x - 1$ 
A)  $f ( x ) = \log _ { 4 } ( x - 1 )$ 
B)  $f ( x ) = \log _ { 4 } x$ 
C)  $f ( x ) = \log _ { 4 } ( x + 1 )$ 
D)  $f ( x ) = \log _ { 4 } x - 1$

Question 20

Approximate the number using a calculator. Round your answer to three decimal places.
-$6 ^ { 3.3 }$

Accepted Answer

A)  $369.742$ 
B)  $19.800$ 
C)  $1291.468$ 
D)  $370.042$ 
A)  $369.742$ 
B)  $19.800$ 
C)  $1291.468$ 
D)  $370.042$

Evaluate the expression without using a calculator. - $\log _ { 10 } 1000$

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. - $\log ( 4 + x ) - \log ( x - 2 ) = \log 3$

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. - $\ln 7 + \ln ( x - 1 ) = 0$

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

Graph the function. -Use the graph of $f ( x ) = \log x$ to obtain the graph of $g ( x ) = 5 - \log x$ . $Graph the function. -Use the graph of f ( x ) = \log x to obtain the graph of g ( x ) = 5 - \log x .$

Solve the exponential equation. Express the solution set in terms of natural logarithms. - $\mathrm { e } ^ { 5 \mathrm { x } } = 8$

Solve the equation by expressing each side as a power of the same base and then equating exponents. - $\mathrm { e } ^ { \mathrm { x } + 5 } = \frac { 1 } { \mathrm { e } ^ { 10 } }$

Evaluate the expression without using a calculator. - $\log _ { 3 } 81$

Solve the problem. -The logistic growth function $f ( t ) = \frac { 800 } { 1 + 10.4 e ^ { - 0.2 t } }$ 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 13 months?

Graph the function. -Use the graph of $f ( x ) = 2 ^ { x }$ to obtain the graph of $g ( x ) = 2 ^ { x + 2 } + 1$ $Graph the function. -Use the graph of f ( x ) = 2 ^ { x } to obtain the graph of g ( x ) = 2 ^ { x + 2 } + 1$

The graph of an exponential function is given. Select the function for the graph from the functions listed. -

Graph the function. - $f(x)=\left(\frac{1}{4}\right)^{x} \text { and } g(x)=\log 1 / 4 x$ $Graph the function. - f(x)=\left(\frac{1}{4}\right)^{x} \text { and } g(x)=\log 1 / 4 x$

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. - $\log _ { 9 } 7 + \log _ { 9 } x = 1$

Graph the function. -Use the graph of $\log _ { 5 } x$ to obtain the graph of $f ( x ) = 2 \log _ { 5 } x$ . $Graph the function. -Use the graph of \log _ { 5 } x to obtain the graph of f ( x ) = 2 \log _ { 5 } x .$

The graph of a logarithmic function is given. Select the function for the graph from the options. -

Approximate the number using a calculator. Round your answer to three decimal places. - $6 ^ { 3.3 }$

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Exam 4: Exponential and Logarithmic Functions

Evaluate the expression without using a calculator. - log⁡101000\log _ { 10 } 1000log10​1000

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⁡7+ln⁡(x−1)=0\ln 7 + \ln ( x - 1 ) = 0ln7+ln(x−1)=0

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. - log⁡5(5x)\log _ { 5 } \left( \frac { 5 } { x } \right)log5​(x5​)

Graph the function. - Use the graph of f(x)=ex to obtain the graph of g(x)=13ex. \text { Use the graph of } f ( x ) = e ^ { x } \text { to obtain the graph of } g ( x ) = \frac { 1 } { 3 } e ^ { x } \text {. } Use the graph of f(x)=ex to obtain the graph of g(x)=31​ex.

Graph the function. -Use the graph of f(x)=log⁡xf ( x ) = \log xf(x)=logx to obtain the graph of g(x)=5−log⁡xg ( x ) = 5 - \log xg(x)=5−logx .

Solve the exponential equation. Express the solution set in terms of natural logarithms. - e5x=8\mathrm { e } ^ { 5 \mathrm { x } } = 8e5x=8

Solve the equation by expressing each side as a power of the same base and then equating exponents. - ex+5=1e10\mathrm { e } ^ { \mathrm { x } + 5 } = \frac { 1 } { \mathrm { e } ^ { 10 } }ex+5=e101​

Evaluate the expression without using a calculator. - log⁡381\log _ { 3 } 81log3​81

Graph the function. -Use the graph of f(x)=2xf ( x ) = 2 ^ { x }f(x)=2x to obtain the graph of g(x)=2x+2+1g ( x ) = 2 ^ { x + 2 } + 1g(x)=2x+2+1

The graph of an exponential function is given. Select the function for the graph from the functions listed. -

Graph the function. - f(x)=(14)x and g(x)=log⁡1/4xf(x)=\left(\frac{1}{4}\right)^{x} \text { and } g(x)=\log 1 / 4 xf(x)=(41​)x and g(x)=log1/4x

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⁡97+log⁡9x=1\log _ { 9 } 7 + \log _ { 9 } x = 1log9​7+log9​x=1

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

The graph of a logarithmic function is given. Select the function for the graph from the options. -

Approximate the number using a calculator. Round your answer to three decimal places. - 63.36 ^ { 3.3 }63.3

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Systems of Equations and Inequalities

Matrices and Determinants

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Filters

Evaluate the expression without using a calculator. - $\log _ { 10 } 1000$

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. - $\ln 7 + \ln ( x - 1 ) = 0$

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

Graph the function. -Use the graph of $f ( x ) = \log x$ to obtain the graph of $g ( x ) = 5 - \log x$ . $Graph the function. -Use the graph of f ( x ) = \log x to obtain the graph of g ( x ) = 5 - \log x .$

Solve the exponential equation. Express the solution set in terms of natural logarithms. - $\mathrm { e } ^ { 5 \mathrm { x } } = 8$

Solve the equation by expressing each side as a power of the same base and then equating exponents. - $\mathrm { e } ^ { \mathrm { x } + 5 } = \frac { 1 } { \mathrm { e } ^ { 10 } }$

Evaluate the expression without using a calculator. - $\log _ { 3 } 81$

Graph the function. -Use the graph of $f ( x ) = 2 ^ { x }$ to obtain the graph of $g ( x ) = 2 ^ { x + 2 } + 1$ $Graph the function. -Use the graph of f ( x ) = 2 ^ { x } to obtain the graph of g ( x ) = 2 ^ { x + 2 } + 1$

Graph the function. - $f(x)=\left(\frac{1}{4}\right)^{x} \text { and } g(x)=\log 1 / 4 x$ $Graph the function. - f(x)=\left(\frac{1}{4}\right)^{x} \text { and } g(x)=\log 1 / 4 x$

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. - $\log _ { 9 } 7 + \log _ { 9 } x = 1$

Graph the function. -Use the graph of $\log _ { 5 } x$ to obtain the graph of $f ( x ) = 2 \log _ { 5 } x$ . $Graph the function. -Use the graph of \log _ { 5 } x to obtain the graph of f ( x ) = 2 \log _ { 5 } x .$

Approximate the number using a calculator. Round your answer to three decimal places. - $6 ^ { 3.3 }$