Question 1

Solve the equation. Round to the nearest thousandth.
-$$e ^ { 4 x } e ^ { 4 x } = e ^ { 4 }$$

Accepted Answer

A)  $\{ 0.643 \}$ 
B)  $\{ 1.640 \}$ 
C)  $\{ - 0.640 \}$ 
D)  $\{ 0.500 \}$ 
A)  $\{ 0.643 \}$ 
B)  $\{ 1.640 \}$ 
C)  $\{ - 0.640 \}$ 
D)  $\{ 0.500 \}$

Question 2

Solve the equation. Round to the nearest thousandth.
-$$15 ( 3 - x ) = 23$$

Accepted Answer

A)  $\{ 1.842 \}$ 
B)  $\{ 1.467 \}$ 
C)  $\{ - 1.467 \}$ 
D)  $\{ 3.864 \}$ 
A)  $\{ 1.842 \}$ 
B)  $\{ 1.467 \}$ 
C)  $\{ - 1.467 \}$ 
D)  $\{ 3.864 \}$

Question 3

Use the definition of inverses to determine whether f and g are inverses.
-$f ( x ) = \frac { 1 } { x + 6 } , \quad g ( x ) = \frac { 6 x + 1 } { x }$

Accepted Answer

A)  No 
B)  Yes 
A)  No 
B)  Yes

Question 4

Provide an appropriate response.
-Use the properties of exponents to write the function of the form $\mathrm { f } ( \mathrm { t } ) = \mathrm { ka } ^ { \mathrm { t } }$, where $\mathrm { k }$ is a constant. $f ( t ) = 3 ^ { 3 t + 2 }$

Accepted Answer

A)  $f ( t ) = 9 \cdot 27 ^ { t }$ 
B)  $f ( t ) = 27 ^ { t } + 9$ 
C)  $f ( t ) = 27 \cdot 9 ^ { t }$ 
D)  $f ( t ) = 9 \cdot 3 ^ { 3 t }$ 
A)  $f ( t ) = 9 \cdot 27 ^ { t }$ 
B)  $f ( t ) = 27 ^ { t } + 9$ 
C)  $f ( t ) = 27 \cdot 9 ^ { t }$ 
D)  $f ( t ) = 9 \cdot 3 ^ { 3 t }$

Question 5

Find the value. Give an approximation to four decimal places.
-$$\ln \left( \frac { 98 } { 18 } \right)$$

Accepted Answer

A)  $7.4753$ 
B)  $1.6946$ 
C)  $1.5863$ 
D)  $- 3.4887$ 
A)  $7.4753$ 
B)  $1.6946$ 
C)  $1.5863$ 
D)  $- 3.4887$

Question 6

Solve the equation and express the solution in exact form.
-$$\log _ { 2 } x ^ { 2 } = \left( \log _ { 2 } x \right) ^ { 2 }$$

Accepted Answer

A)  $\{ 0,2 \}$ 
B)  $\{ 4 \}$ 
C)  $\{ 1,2 \}$ 
D)  $\{ 1,4 \}$ 
A)  $\{ 0,2 \}$ 
B)  $\{ 4 \}$ 
C)  $\{ 1,2 \}$ 
D)  $\{ 1,4 \}$

Question 7

Use the graph of f to sketch a graph of the inverse of f using a dashed curve.
-

Accepted Answer

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

Question 8

Use properties of logarithms to evaluate the expression.
-Let $\mathrm { u } = \ln \mathrm { a }$ and $\mathrm { v } = \ln \mathrm { b }$. Write the following expression in terms of $\mathrm { u }$ and $\mathrm { v }$ without using the funct $\ln \sqrt [ 3 ] { \frac { a ^ { 5 } } { b ^ { 7 } } }$

Accepted Answer

A)  $15 u - 21 v$ 
B)  $5 u - 7 v$ 
C)  $\frac { 5 } { 3 } u - \frac { 7 } { 3 } v$ 
D)  $15 u + 21 v$ n ln.286) 
A)  $15 u - 21 v$ 
B)  $5 u - 7 v$ 
C)  $\frac { 5 } { 3 } u - \frac { 7 } { 3 } v$ 
D)  $15 u + 21 v$ n ln.286)

Question 9

Choose the one alternative that best completes the statement or answers the question.
-Many states have passed laws against smoking in public places since January. The total number of states, $\mathrm { N }$, that have passed a no smoking law, $\mathrm { t }$ months after January is given by the function $\mathrm { N } ( \mathrm { t } ) = \frac { 50 } { 1 + 19 \mathrm { e } ^ { - 0.7 \mathrm { t } } }$. How many states had passed a law in January? Round to the nearest thousandth.

Accepted Answer

A)  0 
B)  $2.5$ 
C)  $0.25$ 
D)  $1.25$ 
A)  0 
B)  $2.5$ 
C)  $0.25$ 
D)  $1.25$

Question 10

Match the function with its graph.
-$$f ( x ) = \log _ { 2 } x$$

Accepted Answer

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

Question 11

Solve the problem.
-$$\mathrm { p } ( \mathrm { t } ) = 2346 \mathrm { e } ^ { 0.003 \mathrm { t } }$$ , where t is the number of years. Use this formula to calculate the population after 10 years.

Accepted Answer

A)  4835 
B)  7252 
C)  2491 
D)  2417 
A)  4835 
B)  7252 
C)  2491 
D)  2417

Question 12

Match the function with its graph.
-$$f ( x ) = \log _ { 2 } \left( \frac { 1 } { x } \right)$$

Accepted Answer

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

Question 13

Solve the equation and express the solution in exact form.
-$$\ln \mathrm { e } ^ { \mathrm { x } } - \ln \mathrm { e } ^ { 5 } = \ln \mathrm { e } ^ { 8 }$$

Accepted Answer

A)  {-3} 
B)  {3} 
C)  {13} 
D)  {40} 
A)  {-3} 
B)  {3} 
C)  {13} 
D)  {40}

Question 14

Decide whether the given functions are inverses.
-$$\begin{array} { l } 
f = \{ ( 5,13 ) , ( 4,0 ) , ( 0,20 ) , ( 13,5 ) \} \
g = \{ ( 13,5 ) , ( 0,4 ) , ( 20,0 ) , ( 5,13 ) \}
\end{array}$$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 15

Use properties of logarithms to evaluate the expression.
-If $\mathrm { f } ( \mathrm { x } ) = \ln \mathrm { x }$, find $\mathrm { f } \left( \mathrm { e } ^ { 18 \ln 11 } \right)$

Accepted Answer

A)  $18 \ln 11$ 
B)  $\mathrm { e } ^ { 11 }$ 
C)  $\ln 11$ 
D)  $11 \ln 18$ 
A)  $18 \ln 11$ 
B)  $\mathrm { e } ^ { 11 }$ 
C)  $\ln 11$ 
D)  $11 \ln 18$

Question 16

Find the value. Give an approximation to four decimal places.
-$$\log \left( \frac { 682 } { 249 } \right)$$

Accepted Answer

A)  $0.4376$ 
B)  $1.1826$ 
C)  $12.0425$ 
D)  $1.0076$ 
A)  $0.4376$ 
B)  $1.1826$ 
C)  $12.0425$ 
D)  $1.0076$

Question 17

Use properties of logarithms to evaluate the expression.
-Let $\mathrm { u } = \ln \mathrm { a }$ and $\mathrm { v } = \ln \mathrm { b }$. Write the following expression in terms of $\mathrm { u }$ and $\mathrm { v }$ without using the funct $\ln \left( \sqrt [ 5 ] { a b ^ { 4 } } \right)$

Accepted Answer

A)  $\frac { \mathrm { u } } { 5 } + \frac { 4 } { 5 } \mathrm { v }$ 
B)  $\frac { \mathrm { u } } { 5 } - \frac { 4 } { 5 } \mathrm { v }$ 
C)  $\frac { 4 } { 5 } \mathrm { u } + \frac { 4 } { 5 } \mathrm { v }$ 
D)  $\frac { \mathrm { u } } { 5 } - 4 \mathrm { v }$ n ln.287) 
A)  $\frac { \mathrm { u } } { 5 } + \frac { 4 } { 5 } \mathrm { v }$ 
B)  $\frac { \mathrm { u } } { 5 } - \frac { 4 } { 5 } \mathrm { v }$ 
C)  $\frac { 4 } { 5 } \mathrm { u } + \frac { 4 } { 5 } \mathrm { v }$ 
D)  $\frac { \mathrm { u } } { 5 } - 4 \mathrm { v }$ n ln.287)

Question 18

Solve the problem.
-The population growth of an animal species is described by $$F ( t ) = 400 \log ( 2 t + 3 )$$ where t is measured in months. Find the population of this species in an area 6 months after the species is
Introduced.

Accepted Answer

A)  470 
B)  704 
C)  74 
D)  240 
A)  470 
B)  704 
C)  74 
D)  240

Question 19

Solve the equation. Round to the nearest thousandth.
-$$4 ^ { x } = 12$$

Accepted Answer

A)  $\{ 3.000 \}$ 
B)  $\{ 1.792 \}$ 
C)  $\{ 0.558 \}$ 
D)  $\{ 1.099 \}$ 
A)  $\{ 3.000 \}$ 
B)  $\{ 1.792 \}$ 
C)  $\{ 0.558 \}$ 
D)  $\{ 1.099 \}$

Question 20

Solve the equation.
-$$( \sqrt { 5 } ) ^ { x + 5 } = 25 ^ { x }$$

Accepted Answer

A)  $\left\{ \frac { 5 } { 3 } \right\}$ 
B)  $\{ 1 \}$ 
C)  $\left\{ \frac { 10 } { 3 } \right\}$ 
D)  $\{ 5 \}$ 
A)  $\left\{ \frac { 5 } { 3 } \right\}$ 
B)  $\{ 1 \}$ 
C)  $\left\{ \frac { 10 } { 3 } \right\}$ 
D)  $\{ 5 \}$

Solve the equation. Round to the nearest thousandth. - $e ^ { 4 x } e ^ { 4 x } = e ^ { 4 }$

Solve the equation. Round to the nearest thousandth. - $15 ( 3 - x ) = 23$

Use the definition of inverses to determine whether f and g are inverses. - $f ( x ) = \frac { 1 } { x + 6 } , \quad g ( x ) = \frac { 6 x + 1 } { x }$

Provide an appropriate response. -Use the properties of exponents to write the function of the form $\mathrm { f } ( \mathrm { t } ) = \mathrm { ka } ^ { \mathrm { t } }$ , where $\mathrm { k }$ is a constant. $f ( t ) = 3 ^ { 3 t + 2 }$

Find the value. Give an approximation to four decimal places. - $\ln \left( \frac { 98 } { 18 } \right)$

Solve the equation and express the solution in exact form. - $\log _ { 2 } x ^ { 2 } = \left( \log _ { 2 } x \right) ^ { 2 }$

Use the graph of f to sketch a graph of the inverse of f using a dashed curve. -

Use properties of logarithms to evaluate the expression. -Let $\mathrm { u } = \ln \mathrm { a }$ and $\mathrm { v } = \ln \mathrm { b }$ . Write the following expression in terms of $\mathrm { u }$ and $\mathrm { v }$ without using the funct $\ln \sqrt [ 3 ] { \frac { a ^ { 5 } } { b ^ { 7 } } }$

Match the function with its graph. - $f ( x ) = \log _ { 2 } x$

Solve the problem. - $\mathrm { p } ( \mathrm { t } ) = 2346 \mathrm { e } ^ { 0.003 \mathrm { t } }$ , where t is the number of years. Use this formula to calculate the population after 10 years.

Match the function with its graph. - $f ( x ) = \log _ { 2 } \left( \frac { 1 } { x } \right)$

Solve the equation and express the solution in exact form. - $\ln \mathrm { e } ^ { \mathrm { x } } - \ln \mathrm { e } ^ { 5 } = \ln \mathrm { e } ^ { 8 }$

Decide whether the given functions are inverses. - f=\{(5,13),(4,0),(0,20),(13,5)\} g=\{(13,5),(0,4),(20,0),(5,13)\}

Use properties of logarithms to evaluate the expression. -If $\mathrm { f } ( \mathrm { x } ) = \ln \mathrm { x }$ , find $\mathrm { f } \left( \mathrm { e } ^ { 18 \ln 11 } \right)$

Find the value. Give an approximation to four decimal places. - $\log \left( \frac { 682 } { 249 } \right)$

Use properties of logarithms to evaluate the expression. -Let $\mathrm { u } = \ln \mathrm { a }$ and $\mathrm { v } = \ln \mathrm { b }$ . Write the following expression in terms of $\mathrm { u }$ and $\mathrm { v }$ without using the funct $\ln \left( \sqrt [ 5 ] { a b ^ { 4 } } \right)$

Solve the problem. -The population growth of an animal species is described by $F ( t ) = 400 \log ( 2 t + 3 )$ where t is measured in months. Find the population of this species in an area 6 months after the species is Introduced.

Solve the equation. Round to the nearest thousandth. - $4 ^ { x } = 12$

Solve the equation. - $( \sqrt { 5 } ) ^ { x + 5 } = 25 ^ { x }$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 5: Inverse, Exponential, and Logarithmic Functions

Solve the equation. Round to the nearest thousandth. - e4xe4x=e4e ^ { 4 x } e ^ { 4 x } = e ^ { 4 }e4xe4x=e4

Solve the equation. Round to the nearest thousandth. - 15(3−x)=2315 ( 3 - x ) = 2315(3−x)=23

Use the definition of inverses to determine whether f and g are inverses. - f(x)=1x+6,g(x)=6x+1xf ( x ) = \frac { 1 } { x + 6 } , \quad g ( x ) = \frac { 6 x + 1 } { x }f(x)=x+61​,g(x)=x6x+1​

Provide an appropriate response. -Use the properties of exponents to write the function of the form f(t)=kat\mathrm { f } ( \mathrm { t } ) = \mathrm { ka } ^ { \mathrm { t } }f(t)=kat , where k\mathrm { k }k is a constant. f(t)=33t+2f ( t ) = 3 ^ { 3 t + 2 }f(t)=33t+2

Find the value. Give an approximation to four decimal places. - ln⁡(9818)\ln \left( \frac { 98 } { 18 } \right)ln(1898​)

Solve the equation and express the solution in exact form. - log⁡2x2=(log⁡2x)2\log _ { 2 } x ^ { 2 } = \left( \log _ { 2 } x \right) ^ { 2 }log2​x2=(log2​x)2

Use the graph of f to sketch a graph of the inverse of f using a dashed curve. -

Match the function with its graph. - f(x)=log⁡2xf ( x ) = \log _ { 2 } xf(x)=log2​x

Solve the problem. - p(t)=2346e0.003t\mathrm { p } ( \mathrm { t } ) = 2346 \mathrm { e } ^ { 0.003 \mathrm { t } }p(t)=2346e0.003t , where t is the number of years. Use this formula to calculate the population after 10 years.

Match the function with its graph. - f(x)=log⁡2(1x)f ( x ) = \log _ { 2 } \left( \frac { 1 } { x } \right)f(x)=log2​(x1​)

Solve the equation and express the solution in exact form. - ln⁡ex−ln⁡e5=ln⁡e8\ln \mathrm { e } ^ { \mathrm { x } } - \ln \mathrm { e } ^ { 5 } = \ln \mathrm { e } ^ { 8 }lnex−lne5=lne8

Decide whether the given functions are inverses. - f=\{(5,13),(4,0),(0,20),(13,5)\} g=\{(13,5),(0,4),(20,0),(5,13)\}

Use properties of logarithms to evaluate the expression. -If f(x)=ln⁡x\mathrm { f } ( \mathrm { x } ) = \ln \mathrm { x }f(x)=lnx , find f(e18ln⁡11)\mathrm { f } \left( \mathrm { e } ^ { 18 \ln 11 } \right)f(e18ln11)

Find the value. Give an approximation to four decimal places. - log⁡(682249)\log \left( \frac { 682 } { 249 } \right)log(249682​)

Solve the problem. -The population growth of an animal species is described by F(t)=400log⁡(2t+3)F ( t ) = 400 \log ( 2 t + 3 )F(t)=400log(2t+3) where t is measured in months. Find the population of this species in an area 6 months after the species is Introduced.

Solve the equation. Round to the nearest thousandth. - 4x=124 ^ { x } = 124x=12

Solve the equation. - (5)x+5=25x( \sqrt { 5 } ) ^ { x + 5 } = 25 ^ { x }(5​)x+5=25x

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Solve the equation. Round to the nearest thousandth. - $e ^ { 4 x } e ^ { 4 x } = e ^ { 4 }$

Solve the equation. Round to the nearest thousandth. - $15 ( 3 - x ) = 23$

Use the definition of inverses to determine whether f and g are inverses. - $f ( x ) = \frac { 1 } { x + 6 } , \quad g ( x ) = \frac { 6 x + 1 } { x }$

Provide an appropriate response. -Use the properties of exponents to write the function of the form $\mathrm { f } ( \mathrm { t } ) = \mathrm { ka } ^ { \mathrm { t } }$ , where $\mathrm { k }$ is a constant. $f ( t ) = 3 ^ { 3 t + 2 }$

Find the value. Give an approximation to four decimal places. - $\ln \left( \frac { 98 } { 18 } \right)$

Solve the equation and express the solution in exact form. - $\log _ { 2 } x ^ { 2 } = \left( \log _ { 2 } x \right) ^ { 2 }$

Match the function with its graph. - $f ( x ) = \log _ { 2 } x$

Solve the problem. - $\mathrm { p } ( \mathrm { t } ) = 2346 \mathrm { e } ^ { 0.003 \mathrm { t } }$ , where t is the number of years. Use this formula to calculate the population after 10 years.

Match the function with its graph. - $f ( x ) = \log _ { 2 } \left( \frac { 1 } { x } \right)$

Solve the equation and express the solution in exact form. - $\ln \mathrm { e } ^ { \mathrm { x } } - \ln \mathrm { e } ^ { 5 } = \ln \mathrm { e } ^ { 8 }$

Use properties of logarithms to evaluate the expression. -If $\mathrm { f } ( \mathrm { x } ) = \ln \mathrm { x }$ , find $\mathrm { f } \left( \mathrm { e } ^ { 18 \ln 11 } \right)$

Find the value. Give an approximation to four decimal places. - $\log \left( \frac { 682 } { 249 } \right)$

Solve the problem. -The population growth of an animal species is described by $F ( t ) = 400 \log ( 2 t + 3 )$ where t is measured in months. Find the population of this species in an area 6 months after the species is Introduced.

Solve the equation. Round to the nearest thousandth. - $4 ^ { x } = 12$

Solve the equation. - $( \sqrt { 5 } ) ^ { x + 5 } = 25 ^ { x }$