Question 1

Determine whether or not the function is one-to-one.
-

Accepted Answer

A) True 
 B)False

Question 2

Evaluate the logarithm.
-$\log _ { 9 } ( - 1 )$

Accepted Answer

A)  1 
B)  $- 1$ 
C)  Undefined 
D)  0 
A)  1 
B)  $- 1$ 
C)  Undefined 
D)  0

Question 3

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth.
-$$e ^ { x } = 5 ^ { x + 4 }$$

Accepted Answer

A)  $\{ - 10.56 \}$ 
B)  $\{ 2.47 \}$ 
C)  $\{ 10.56 \}$ 
D)  $\{ - 32.82 \}$ 
A)  $\{ - 10.56 \}$ 
B)  $\{ 2.47 \}$ 
C)  $\{ 10.56 \}$ 
D)  $\{ - 32.82 \}$

Question 4

Determine whether or not the function is one-to-one.
-$f ( x ) = \frac { - 7 x - 7 } { 7 x - 3 }$

Accepted Answer

A) True 
 B)False

Question 5

Provide an appropriate response.
-The graph of an exponential function with base a is given. Sketch the graph of $g ( x ) = - a x$. Give the domain and range of $g$.
$f(x)=a^{X}$

Accepted Answer

The answer of Provide an appropriate response.
-The graph of an...

Question 6

Solve for the indicated variable.
-$I = \frac { \mathrm { w } } { \mathrm { P } } \left( 1 - \mathrm { e } ^ { - \mathrm { as } / 3 } \right)$, for $\mathrm { s }$

Accepted Answer

A)  $s = - \frac { 3 \ln \left( 1 - I P _ { W } \right) } { a }$ 
B)  $s = - \frac { 3 } { a } \ln \left( 1 - \frac { \mathrm { IP } } { \mathrm { w } } \right)$ 
C)  $\mathrm { s } = \frac { \mathrm { IwP } \cdot \ln ( 1 - \mathrm { a } ) } { 3 }$ 
D)  $\mathrm { s } = \frac { 3 \cdot \ln ( 1 - \mathrm { a } ) } { \mathrm { IwP } }$ 
A)  $s = - \frac { 3 \ln \left( 1 - I P _ { W } \right) } { a }$ 
B)  $s = - \frac { 3 } { a } \ln \left( 1 - \frac { \mathrm { IP } } { \mathrm { w } } \right)$ 
C)  $\mathrm { s } = \frac { \mathrm { IwP } \cdot \ln ( 1 - \mathrm { a } ) } { 3 }$ 
D)  $\mathrm { s } = \frac { 3 \cdot \ln ( 1 - \mathrm { a } ) } { \mathrm { IwP } }$

Question 7

The population growth of an animal species is described by $\mathrm { F } ( \mathrm { t } ) = 400 \log ( 2 \mathrm { t } + 3 )$ 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)  704 
B)  470 
C)  74 
D)  240 
A)  704 
B)  470 
C)  74 
D)  240

Question 8

Given that $f ( x ) = 5 \ln 2 x$, find $f ^ { - 1 } ( x )$ and give the domain and range of $f ^ { - 1 } ( x )$.

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 2 } \mathrm { e } ^ { \mathrm { x } - 5 }$, domain $= ( 0 , \infty )$, range $= ( - \infty , \infty )$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 2 } \mathrm { e } ^ { \mathrm { x } / 5 }$, domain $= ( - \infty , \infty )$, range $= ( 0 , \infty )$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 2 } \mathrm { e } ^ { \mathrm { x } / 5 }$, domain $= ( 0 , \infty )$, range $= ( - \infty , \infty )$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 2 } \mathrm { e } ^ { \mathrm { x } - 5 }$, domain $= ( - \infty , \infty )$, range $= ( 0 , \infty )$ 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 2 } \mathrm { e } ^ { \mathrm { x } - 5 }$, domain $= ( 0 , \infty )$, range $= ( - \infty , \infty )$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 2 } \mathrm { e } ^ { \mathrm { x } / 5 }$, domain $= ( - \infty , \infty )$, range $= ( 0 , \infty )$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 2 } \mathrm { e } ^ { \mathrm { x } / 5 }$, domain $= ( 0 , \infty )$, range $= ( - \infty , \infty )$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 2 } \mathrm { e } ^ { \mathrm { x } - 5 }$, domain $= ( - \infty , \infty )$, range $= ( 0 , \infty )$

Question 9

Find the function value. If the result is irrational, round your answer to the nearest thousandth.
-$\text { Let } f ( x ) = 4 ^ { x } \text {. Find } f ( 3 )$

Accepted Answer

A)  12 
B)  81 
C)  256 
D)  64 
A)  12 
B)  81 
C)  256 
D)  64

Question 10

Use the change of base rule to find the logarithm to four decimal places.
-$\log _ { 2 } 36.87$

Accepted Answer

A)  18.4350 
B)  0.1921 
C)  5.2044 
D)  1.5667 
A)  18.4350 
B)  0.1921 
C)  5.2044 
D)  1.5667

Question 11

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 12

A population is increasing according to the exponential function defined by $\mathrm { y } = 3 \mathrm { e } .04 \mathrm { x }$, where $\mathrm { y }$ is in millions and $x$ is the number of years. Which of the following should be done in order to answer the question "How long will it take for the population to quadruple?"

Accepted Answer

A)  Evaluate $\mathrm { y } = 3 \mathrm { e } \cdot 04 ( 4 )$. 
B)  Solve $3 \mathrm { e } ^ { - 04 \mathrm { x } } = 4$. 
C)  Evaluate $y = 3 e ^ { 0 } 04 ( 1 / 4 )$. 
D)  Solve $3 e ^ { . } 04 x = 12$. 
A)  Evaluate $\mathrm { y } = 3 \mathrm { e } \cdot 04 ( 4 )$. 
B)  Solve $3 \mathrm { e } ^ { - 04 \mathrm { x } } = 4$. 
C)  Evaluate $y = 3 e ^ { 0 } 04 ( 1 / 4 )$. 
D)  Solve $3 e ^ { . } 04 x = 12$.

Question 13

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $a \neq 1 \text { and } b \neq 1$ .
-$\log _ { 3 } m + \log 3 n$

Accepted Answer

A)  $\log _ { 3 } \mathrm { mn }$ 
B)  $\log _ { 3 } ( m + n )$ 
C)  $\log _ { 3 } m \cdot \log _ { 3 } n$ 
D)  $\log _ { 3 } \left( \frac { \mathrm { m } } { \mathrm { n } } \right)$ 
A)  $\log _ { 3 } \mathrm { mn }$ 
B)  $\log _ { 3 } ( m + n )$ 
C)  $\log _ { 3 } m \cdot \log _ { 3 } n$ 
D)  $\log _ { 3 } \left( \frac { \mathrm { m } } { \mathrm { n } } \right)$

Question 14

A certain radioactive isotope decays at a rate of 0.175% annually. Determine the half-life of this isotope, to the nearest year.

Accepted Answer

A)  396 yr 
B)  172 yr 
C)  4 yr 
D)  286 yr 
A)  396 yr 
B)  172 yr 
C)  4 yr 
D)  286 yr

Question 15

Round to the nearest thousandth.
-$$3 e ^ { ( 4 x - 4 ) } = 18$$

Accepted Answer

A)  $\{ 5.500 \}$ 
B)  $\{ 1.241 \}$ 
C)  $\{ - 0.552 \}$ 
D)  $\{ 1.448 \}$ 
A)  $\{ 5.500 \}$ 
B)  $\{ 1.241 \}$ 
C)  $\{ - 0.552 \}$ 
D)  $\{ 1.448 \}$

Question 16

Solve the equation and express the solution in exact form.
-$\ln 2 x + \ln 9 x = \ln 19$

Accepted Answer

A)  $\{ 0 \}$ 
B)  $\left\{ \frac { \mathrm { e } ^ { 19 } } { 18 } \right\}$ 
C)  $\{ 1 \}$ 
D)  $\left\{ \left( \frac { 19 } { 18 } \right) ^ { 1 / 2 } \right\}$ 
A)  $\{ 0 \}$ 
B)  $\left\{ \frac { \mathrm { e } ^ { 19 } } { 18 } \right\}$ 
C)  $\{ 1 \}$ 
D)  $\left\{ \left( \frac { 19 } { 18 } \right) ^ { 1 / 2 } \right\}$

Question 17

Given $\log _ { 10 } 2 \approx 0.3010 \text { and } \log _ { 10 } 3 \approx 0.4771$ find the logarithm without using a calculator.
-$\log _ { 10 } 24$

Accepted Answer

A)  0.4308 
B)  1.3801 
C)  1.7323 
D)  0.5044 
A)  0.4308 
B)  1.3801 
C)  1.7323 
D)  0.5044

Question 18

Solve the equation and express the solution in exact form.
-$\log ( 4 + x ) - \log ( x - 3 ) = \log 2$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ 10 \}$ 
C)  $\{ - 10 \}$ 
D)  $\left\{ \frac { 1 } { 2 } \right\}$ 
A)  $\varnothing$ 
B)  $\{ 10 \}$ 
C)  $\{ - 10 \}$ 
D)  $\left\{ \frac { 1 } { 2 } \right\}$

Question 19

Find the present value of the future value.
-$2000, invested for 9 years at 5% compounded monthly

Accepted Answer

A)  $3088.69 
B)  $1276.45 
C)  $1321.45 
D)  $3133.69 
A)  $3088.69 
B)  $1276.45 
C)  $1321.45 
D)  $3133.69

Question 20

Write an equivalent expression in exponential form.
-$$8 x - 56 = \log _ { x } 1$$

Accepted Answer

A)  $\{ 7 \}$ 
B)  $\{ 448 \}$ 
C)  $\{ 48 \}$ 
D)  $\left\{ \frac { 1 } { 7 } \right\}$ 
A)  $\{ 7 \}$ 
B)  $\{ 448 \}$ 
C)  $\{ 48 \}$ 
D)  $\left\{ \frac { 1 } { 7 } \right\}$

Determine whether or not the function is one-to-one. -

Evaluate the logarithm. - $\log _ { 9 } ( - 1 )$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $e ^ { x } = 5 ^ { x + 4 }$

Determine whether or not the function is one-to-one. - $f ( x ) = \frac { - 7 x - 7 } { 7 x - 3 }$

Solve for the indicated variable. - $I = \frac { \mathrm { w } } { \mathrm { P } } \left( 1 - \mathrm { e } ^ { - \mathrm { as } / 3 } \right)$ , for $\mathrm { s }$

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

Given that $f ( x ) = 5 \ln 2 x$ , find $f ^ { - 1 } ( x )$ and give the domain and range of $f ^ { - 1 } ( x )$ .

Find the function value. If the result is irrational, round your answer to the nearest thousandth. - $\text { Let } f ( x ) = 4 ^ { x } \text {. Find } f ( 3 )$

Use the change of base rule to find the logarithm to four decimal places. - $\log _ { 2 } 36.87$

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

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $a \neq 1 \text { and } b \neq 1$ . - $\log _ { 3 } m + \log 3 n$

A certain radioactive isotope decays at a rate of 0.175% annually. Determine the half-life of this isotope, to the nearest year.

Round to the nearest thousandth. - $3 e ^ { ( 4 x - 4 ) } = 18$

Solve the equation and express the solution in exact form. - $\ln 2 x + \ln 9 x = \ln 19$

Given $\log _ { 10 } 2 \approx 0.3010 \text { and } \log _ { 10 } 3 \approx 0.4771$ find the logarithm without using a calculator. - $\log _ { 10 } 24$

Solve the equation and express the solution in exact form. - $\log ( 4 + x ) - \log ( x - 3 ) = \log 2$

Find the present value of the future value. -$2000, invested for 9 years at 5% compounded monthly

Write an equivalent expression in exponential form. - $8 x - 56 = \log _ { x } 1$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 5: Inverse, Exponential, and Logarithmic Functions

Determine whether or not the function is one-to-one. -

Evaluate the logarithm. - log⁡9(−1)\log _ { 9 } ( - 1 )log9​(−1)

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - ex=5x+4e ^ { x } = 5 ^ { x + 4 }ex=5x+4

Determine whether or not the function is one-to-one. - f(x)=−7x−77x−3f ( x ) = \frac { - 7 x - 7 } { 7 x - 3 }f(x)=7x−3−7x−7​

Provide an appropriate response. -The graph of an exponential function with base a is given. Sketch the graph of g(x)=−axg ( x ) = - a xg(x)=−ax . Give the domain and range of ggg . f(x)=aXf(x)=a^{X}f(x)=aX

Solve for the indicated variable. - I=wP(1−e−as/3)I = \frac { \mathrm { w } } { \mathrm { P } } \left( 1 - \mathrm { e } ^ { - \mathrm { as } / 3 } \right)I=Pw​(1−e−as/3) , for s\mathrm { s }s

The population growth of an animal species is described by F(t)=400log⁡(2t+3)\mathrm { F } ( \mathrm { t } ) = 400 \log ( 2 \mathrm { 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.

Given that f(x)=5ln⁡2xf ( x ) = 5 \ln 2 xf(x)=5ln2x , find f−1(x)f ^ { - 1 } ( x )f−1(x) and give the domain and range of f−1(x)f ^ { - 1 } ( x )f−1(x) .

Find the function value. If the result is irrational, round your answer to the nearest thousandth. - Let f(x)=4x. Find f(3)\text { Let } f ( x ) = 4 ^ { x } \text {. Find } f ( 3 ) Let f(x)=4x. Find f(3)

Use the change of base rule to find the logarithm to four decimal places. - log⁡236.87\log _ { 2 } 36.87log2​36.87

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

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with a≠1 and b≠1a \neq 1 \text { and } b \neq 1a=1 and b=1 . - log⁡3m+log⁡3n\log _ { 3 } m + \log 3 nlog3​m+log3n

A certain radioactive isotope decays at a rate of 0.175% annually. Determine the half-life of this isotope, to the nearest year.

Round to the nearest thousandth. - 3e(4x−4)=183 e ^ { ( 4 x - 4 ) } = 183e(4x−4)=18

Solve the equation and express the solution in exact form. - ln⁡2x+ln⁡9x=ln⁡19\ln 2 x + \ln 9 x = \ln 19ln2x+ln9x=ln19

Given log⁡102≈0.3010 and log⁡103≈0.4771\log _ { 10 } 2 \approx 0.3010 \text { and } \log _ { 10 } 3 \approx 0.4771log10​2≈0.3010 and log10​3≈0.4771 find the logarithm without using a calculator. - log⁡1024\log _ { 10 } 24log10​24

Solve the equation and express the solution in exact form. - log⁡(4+x)−log⁡(x−3)=log⁡2\log ( 4 + x ) - \log ( x - 3 ) = \log 2log(4+x)−log(x−3)=log2

Find the present value of the future value. -$2000, invested for 9 years at 5% compounded monthly

Write an equivalent expression in exponential form. - 8x−56=log⁡x18 x - 56 = \log _ { x } 18x−56=logx​1

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Evaluate the logarithm. - $\log _ { 9 } ( - 1 )$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $e ^ { x } = 5 ^ { x + 4 }$

Determine whether or not the function is one-to-one. - $f ( x ) = \frac { - 7 x - 7 } { 7 x - 3 }$

Solve for the indicated variable. - $I = \frac { \mathrm { w } } { \mathrm { P } } \left( 1 - \mathrm { e } ^ { - \mathrm { as } / 3 } \right)$ , for $\mathrm { s }$

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

Given that $f ( x ) = 5 \ln 2 x$ , find $f ^ { - 1 } ( x )$ and give the domain and range of $f ^ { - 1 } ( x )$ .

Find the function value. If the result is irrational, round your answer to the nearest thousandth. - $\text { Let } f ( x ) = 4 ^ { x } \text {. Find } f ( 3 )$

Use the change of base rule to find the logarithm to four decimal places. - $\log _ { 2 } 36.87$

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $a \neq 1 \text { and } b \neq 1$ . - $\log _ { 3 } m + \log 3 n$

Round to the nearest thousandth. - $3 e ^ { ( 4 x - 4 ) } = 18$

Solve the equation and express the solution in exact form. - $\ln 2 x + \ln 9 x = \ln 19$

Given $\log _ { 10 } 2 \approx 0.3010 \text { and } \log _ { 10 } 3 \approx 0.4771$ find the logarithm without using a calculator. - $\log _ { 10 } 24$

Solve the equation and express the solution in exact form. - $\log ( 4 + x ) - \log ( x - 3 ) = \log 2$

Write an equivalent expression in exponential form. - $8 x - 56 = \log _ { x } 1$