Question 1

Write an equivalent expression in exponential form.
-$\log _ { 10 } 10,000,000 = 7$

Accepted Answer

A)  $10,000,000 ^ { 7 } = 10$ 
B)  $710 = 10,000,000$ 
C)  $10 ^ { 7 } = 10,000,000$ 
D)  $1010,000,000 = 7$ 
A)  $10,000,000 ^ { 7 } = 10$ 
B)  $710 = 10,000,000$ 
C)  $10 ^ { 7 } = 10,000,000$ 
D)  $1010,000,000 = 7$

Question 2

Decide whether the pair of functions graphed are inverses.
-

Accepted Answer

A) True 
 B)False

Question 3

Solve the equation and express the solution in exact form.
-$$\ln ( - x ) + \ln 4 = \ln ( 3 x - 9 )$$

Accepted Answer

A)  $\left\{ - \frac { 9 } { 7 } \right\}$ 
B)  $\left\{ \frac { 7 } { 9 } \right\}$ 
C)  $\varnothing$ 
D)  $\left\{ \frac { 9 } { 7 } \right\}$ 
A)  $\left\{ - \frac { 9 } { 7 } \right\}$ 
B)  $\left\{ \frac { 7 } { 9 } \right\}$ 
C)  $\varnothing$ 
D)  $\left\{ \frac { 9 } { 7 } \right\}$

Question 4

Provide an appropriate response.
-Use the properties of exponents to write the function of the form $\mathrm { f } ( \mathrm { t } ) = \mathrm { ka } t$, where $\mathrm { k }$ is a constant.
$$f ( t ) = \left( \frac { 1 } { 3 } \right) ^ { 1 - 2 t }$$

Accepted Answer

A)  $f ( t ) = \frac { 1 } { 3 } \left( \frac { 1 } { 9 } \right) ^ { t }$ 
B)  $f ( t ) = \left( \frac { 1 } { 3 } \right) 9 ^ { t }$ 
C)  $f ( t ) = 3 \cdot 9 t$ 
D)  $f ( t ) = \left( \frac { 1 } { 9 } \right) 3 ^ { t }$ 
A)  $f ( t ) = \frac { 1 } { 3 } \left( \frac { 1 } { 9 } \right) ^ { t }$ 
B)  $f ( t ) = \left( \frac { 1 } { 3 } \right) 9 ^ { t }$ 
C)  $f ( t ) = 3 \cdot 9 t$ 
D)  $f ( t ) = \left( \frac { 1 } { 9 } \right) 3 ^ { t }$

Question 5

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

Question 6

Solve the equation.
-$$64 ^ { x - 1 } = 16 ^ { 3 x }$$

Accepted Answer

A)  $\{ - 1 \}$ 
B)  $\{ - 6 \rangle$ 
C)  $\left\{ - \frac { 1 } { 6 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 2 } \right\}$ 
A)  $\{ - 1 \}$ 
B)  $\{ - 6 \rangle$ 
C)  $\left\{ - \frac { 1 } { 6 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 2 } \right\}$

Question 7

Find the future value.
-$4383.95 invested for 12 years at 5% compounded monthly

Accepted Answer

A)  $7978.13 
B)  $7958.42 
C)  $7929.36 
D)  $7872.94 
A)  $7978.13 
B)  $7958.42 
C)  $7929.36 
D)  $7872.94

Question 8

Suppose the consumption of electricity grows at 4.4% per year, compounded continuously. Find the number of years before the use of electricity has tripled. Round the answer to the nearest hundredth.

Accepted Answer

A)  0.25 yr 
B)  68.18 yr 
C)  2.50 yr 
D)  24.97 yr 
A)  0.25 yr 
B)  68.18 yr 
C)  2.50 yr 
D)  24.97 yr

Question 9

Find the required annual interest rate, to the nearest tenth of a percent, for $1200 to grow to $1500 if interest is compounded monthly for 6 years.

Accepted Answer

A)  7.4% 
B)  0.3% 
C)  2.5% 
D)  3.7% 
A)  7.4% 
B)  0.3% 
C)  2.5% 
D)  3.7%

Question 10

Round to the nearest thousandth.
-$$5 ( 3 - x ) = 22$$

Accepted Answer

A)  $\{ 1.400 \}$ 
B)  $\{ 1.079 \}$ 
C)  $\{ 3.521 \}$ 
D)  $\{ - 1.400 \}$ 
A)  $\{ 1.400 \}$ 
B)  $\{ 1.079 \}$ 
C)  $\{ 3.521 \}$ 
D)  $\{ - 1.400 \}$

Question 11

Find the value. Give an approximation to four decimal places.
-log 273

Accepted Answer

A)  2.4378 
B)  5.6095 
C)  2.4362 
D)  2.4346 
A)  2.4378 
B)  5.6095 
C)  2.4362 
D)  2.4346

Question 12

The growth in population of a city can be seen using the formula p(t) $\mathrm { p } ( \mathrm { t } ) = 9768 \mathrm { e } ^ { 0.003 \mathrm { t } }$ , where t is the number of years. According to this formula, in how many years will the population reach 14,652? Round to the nearest
Tenth of a year.

Accepted Answer

A)  270.3 yr 
B)  135.2 yr 
C)  67.6 yr 
D)  101.4 yr 
A)  270.3 yr 
B)  135.2 yr 
C)  67.6 yr 
D)  101.4 yr

Question 13

Solve the following graphically. If necessary, round answers to the nearest thousandth.
-$$\mathrm { x } ^ { 2 } - 4 \mathrm { x } - 7 = \mathrm { e } ^ { \mathrm { x } - 6 } - 3$$

Accepted Answer

A)  $\{ - 0.8,4.87 \}$ 
B)  $\{ - 0.03 \}$ 
C)  $\{ - 0.81,4.88 \}$ 
D)  $\{ - 0.83,4.89 \}$ 
A)  $\{ - 0.8,4.87 \}$ 
B)  $\{ - 0.03 \}$ 
C)  $\{ - 0.81,4.88 \}$ 
D)  $\{ - 0.83,4.89 \}$

Question 14

Find the value. Give an approximation to four decimal places.
-ln 0.000743

Accepted Answer

A)  $3.1290$ 
B)  $- 7.2048$ 
C)  $- 3.1290$ 
D)  $7.2048$ 
A)  $3.1290$ 
B)  $- 7.2048$ 
C)  $- 3.1290$ 
D)  $7.2048$

Question 15

Write an equivalent expression in exponential form.
-$\log _ { 1 / 3 } ( x + 5 ) = - 3$

Accepted Answer

A)  22 
B)  27 
C)  32 
D)  42 
A)  22 
B)  27 
C)  32 
D)  42

Question 16

Give the domain and range.
-$f(x)=\log _{5}(x-1)$

Accepted Answer

A)  domain: $( 0 , \infty )$; range: $( \infty , \infty )$
  
B)  domain: $( \infty , \infty )$; range: $( 0 , \infty )$
  
C)  domain: $( 1 , \infty )$; range: $( \infty , \infty )$
  
D)  domain: $( \infty , \infty )$; range: $( - 1 , \infty )$
  
A)  domain: $( 0 , \infty )$; range: $( \infty , \infty )$
  
B)  domain: $( \infty , \infty )$; range: $( 0 , \infty )$
  
C)  domain: $( 1 , \infty )$; range: $( \infty , \infty )$
  
D)  domain: $( \infty , \infty )$; range: $( - 1 , \infty )$

Question 17

Round to the nearest thousandth.
-$$3 ( 3 x - 3 ) = 24$$

Accepted Answer

A)  $\{ - 0.036 \}$ 
B)  $\{ 3.667 \}$ 
C)  $\{ 1.693 \}$ 
D)  $\{ 1.964 \}$ 
A)  $\{ - 0.036 \}$ 
B)  $\{ 3.667 \}$ 
C)  $\{ 1.693 \}$ 
D)  $\{ 1.964 \}$

Question 18

Solve the following graphically. If necessary, round answers to the nearest thousandth.
-$800 ( 1 - 0.04 ) ^ { 12 x } = 200$

Accepted Answer

A)  $\{ - 424.152 \}$ 
B)  $\{ 2.830 \}$ 
C)  $\{ 407.513952 \}$ 
D)  $\{ - 24.462 \}$ 
A)  $\{ - 424.152 \}$ 
B)  $\{ 2.830 \}$ 
C)  $\{ 407.513952 \}$ 
D)  $\{ - 24.462 \}$

Question 19

Between what two integers does the solution of $8 x = 91$ lie? Explain your answer.

Accepted Answer

The soluti

Question 20

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}

Write an equivalent expression in exponential form. - $\log _ { 10 } 10,000,000 = 7$

Decide whether the pair of functions graphed are inverses. -

Solve the equation and express the solution in exact form. - $\ln ( - x ) + \ln 4 = \ln ( 3 x - 9 )$

Provide an appropriate response. -Use the properties of exponents to write the function of the form $\mathrm { f } ( \mathrm { t } ) = \mathrm { ka } t$ , where $\mathrm { k }$ is a constant. $f ( t ) = \left( \frac { 1 } { 3 } \right) ^ { 1 - 2 t }$

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. - $64 ^ { x - 1 } = 16 ^ { 3 x }$

Find the future value. -$4383.95 invested for 12 years at 5% compounded monthly

Suppose the consumption of electricity grows at 4.4% per year, compounded continuously. Find the number of years before the use of electricity has tripled. Round the answer to the nearest hundredth.

Find the required annual interest rate, to the nearest tenth of a percent, for $1200 to grow to $1500 if interest is compounded monthly for 6 years.

Round to the nearest thousandth. - $5 ( 3 - x ) = 22$

Find the value. Give an approximation to four decimal places. -log 273

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $\mathrm { x } ^ { 2 } - 4 \mathrm { x } - 7 = \mathrm { e } ^ { \mathrm { x } - 6 } - 3$

Find the value. Give an approximation to four decimal places. -ln 0.000743

Write an equivalent expression in exponential form. - $\log _ { 1 / 3 } ( x + 5 ) = - 3$

Give the domain and range. - $f(x)=\log _{5}(x-1)$ $Give the domain and range. - f(x)=\log _{5}(x-1)$

Round to the nearest thousandth. - $3 ( 3 x - 3 ) = 24$

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $800 ( 1 - 0.04 ) ^ { 12 x } = 200$

Between what two integers does the solution of $8 x = 91$ lie? Explain your answer.

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

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

Write an equivalent expression in exponential form. - log⁡1010,000,000=7\log _ { 10 } 10,000,000 = 7log10​10,000,000=7

Decide whether the pair of functions graphed are inverses. -

Solve the equation and express the solution in exact form. - ln⁡(−x)+ln⁡4=ln⁡(3x−9)\ln ( - x ) + \ln 4 = \ln ( 3 x - 9 )ln(−x)+ln4=ln(3x−9)

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 } tf(t)=kat , where k\mathrm { k }k is a constant. f(t)=(13)1−2tf ( t ) = \left( \frac { 1 } { 3 } \right) ^ { 1 - 2 t }f(t)=(31​)1−2t

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 ttt is measured in months. Find the population of this species in an area 6 months after the species is introduced.

Solve the equation. - 64x−1=163x64 ^ { x - 1 } = 16 ^ { 3 x }64x−1=163x

Find the future value. -$4383.95 invested for 12 years at 5% compounded monthly

Suppose the consumption of electricity grows at 4.4% per year, compounded continuously. Find the number of years before the use of electricity has tripled. Round the answer to the nearest hundredth.

Find the required annual interest rate, to the nearest tenth of a percent, for $1200 to grow to $1500 if interest is compounded monthly for 6 years.

Round to the nearest thousandth. - 5(3−x)=225 ( 3 - x ) = 225(3−x)=22

Find the value. Give an approximation to four decimal places. -log 273

Solve the following graphically. If necessary, round answers to the nearest thousandth. - x2−4x−7=ex−6−3\mathrm { x } ^ { 2 } - 4 \mathrm { x } - 7 = \mathrm { e } ^ { \mathrm { x } - 6 } - 3x2−4x−7=ex−6−3

Find the value. Give an approximation to four decimal places. -ln 0.000743

Write an equivalent expression in exponential form. - log⁡1/3(x+5)=−3\log _ { 1 / 3 } ( x + 5 ) = - 3log1/3​(x+5)=−3

Give the domain and range. - f(x)=log⁡5(x−1)f(x)=\log _{5}(x-1)f(x)=log5​(x−1)

Round to the nearest thousandth. - 3(3x−3)=243 ( 3 x - 3 ) = 243(3x−3)=24

Solve the following graphically. If necessary, round answers to the nearest thousandth. - 800(1−0.04)12x=200800 ( 1 - 0.04 ) ^ { 12 x } = 200800(1−0.04)12x=200

Between what two integers does the solution of 8x=918 x = 918x=91 lie? Explain your answer.

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

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

Write an equivalent expression in exponential form. - $\log _ { 10 } 10,000,000 = 7$

Solve the equation and express the solution in exact form. - $\ln ( - x ) + \ln 4 = \ln ( 3 x - 9 )$

Provide an appropriate response. -Use the properties of exponents to write the function of the form $\mathrm { f } ( \mathrm { t } ) = \mathrm { ka } t$ , where $\mathrm { k }$ is a constant. $f ( t ) = \left( \frac { 1 } { 3 } \right) ^ { 1 - 2 t }$

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. - $64 ^ { x - 1 } = 16 ^ { 3 x }$

Round to the nearest thousandth. - $5 ( 3 - x ) = 22$

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $\mathrm { x } ^ { 2 } - 4 \mathrm { x } - 7 = \mathrm { e } ^ { \mathrm { x } - 6 } - 3$

Write an equivalent expression in exponential form. - $\log _ { 1 / 3 } ( x + 5 ) = - 3$

Give the domain and range. - $f(x)=\log _{5}(x-1)$ $Give the domain and range. - f(x)=\log _{5}(x-1)$

Round to the nearest thousandth. - $3 ( 3 x - 3 ) = 24$

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $800 ( 1 - 0.04 ) ^ { 12 x } = 200$

Between what two integers does the solution of $8 x = 91$ lie? Explain your answer.

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