Question 1

Evaluate the logarithm.
-$\log _{3} \sqrt{3}$

Accepted Answer

A)  -2 
B)  $\frac{1}{2}$ 
C)  $-\frac{1}{2}$ 
D)  2 
A)  -2 
B)  $\frac{1}{2}$ 
C)  $-\frac{1}{2}$ 
D)  2

Question 2

Write in exponential form.
-$\log _{x}\left(\frac{81}{256}\right)=4$

Accepted Answer

A)  $\{81\}$ 
B)  $\{4\}$ 
C)  $\left\{\frac{4}{3}\right\}$ 
D)  $\left\{\frac{3}{4}\right\}$ 
A)  $\{81\}$ 
B)  $\{4\}$ 
C)  $\left\{\frac{4}{3}\right\}$ 
D)  $\left\{\frac{3}{4}\right\}$

Question 3

Rewrite the given expression as a single logarithm. Assume that all variables are defined in such a way that variable expressions are positive and bases are positive numbers not equal to 1 .
-$\log _{\mathrm{W}}\left(\mathrm{x}^{2}-16\right)-\log _{\mathrm{W}}(\mathrm{x}-4)$

Accepted Answer

A)  $\log _{W}(x+4)$ 
B)  $\frac{\log _{W}\left(x^{2}-16\right)}{\log _{W}(x-4)}$ 
C)  $\log _{W}\left(x^{2}-16\right)(x-4)$ 
D)  $\log _{W}\left[\left(x^{2}-16\right)-(x-4)\right]$ 
A)  $\log _{W}(x+4)$ 
B)  $\frac{\log _{W}\left(x^{2}-16\right)}{\log _{W}(x-4)}$ 
C)  $\log _{W}\left(x^{2}-16\right)(x-4)$ 
D)  $\log _{W}\left[\left(x^{2}-16\right)-(x-4)\right]$

Question 4

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."
-$\{(-6,8),(-19,8),(-7,-12)\}$

Accepted Answer

A)  $\{(-6,8),(8,-19),(-12,-7)\}$ 
B)  $\{(8,-6),(-7,-19),(-12,8)\}$ 
C)  Not one-to-one 
D)  $\{(8,-6),(8,-19),(-12,-7)\}$ 
A)  $\{(-6,8),(8,-19),(-12,-7)\}$ 
B)  $\{(8,-6),(-7,-19),(-12,8)\}$ 
C)  Not one-to-one 
D)  $\{(8,-6),(8,-19),(-12,-7)\}$

Question 5

In your own words, explain what a logarithm is.

Accepted Answer

Answers may vary. On

Question 6

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."
-$\{(9,-5),(13,6),(19,20)\}$

Accepted Answer

A)  $\{(9,6),(9,13),(20,19)\}$ 
B)  $\{(-5,9),(19,13),(20,6)\}$ 
C)  $\{(-5,9),(6,13),(20,19)\}$ 
D)  Not one-to-one 
A)  $\{(9,6),(9,13),(20,19)\}$ 
B)  $\{(-5,9),(19,13),(20,6)\}$ 
C)  $\{(-5,9),(6,13),(20,19)\}$ 
D)  Not one-to-one

Question 7

Solve the equation. Give the solution to three decimal places.
-$9^{-\mathrm{x}-1}=71$

Accepted Answer

A)  $\{-3.940\}$ 
B)  $\{-1.940\}$ 
C)  $\{-8.366\}$ 
D)  $\{-2.940\}$ 
A)  $\{-3.940\}$ 
B)  $\{-1.940\}$ 
C)  $\{-8.366\}$ 
D)  $\{-2.940\}$

Question 8

The table below gives the actual values of the population of a small island in the Pacific Ocean. The population is modeled by the equation $\mathrm{y}=75.2(1.055)^{\mathrm{x}}$, where $\mathrm{x}=0$ represents the population of the island in 1990.

For the point displayed in the calculator screen above, how does the model compare to the actual?

Accepted Answer

A)  The display indicates that for the year 1993, the model gives a value of about 87 people, which is slightly less than the actual value of 88 people. 
B)  The display indicates that for the year 1990, the model gives a value of 75.2 people, which is slightly more than the actual value of 75 people. 
C)  The display indicates that for the year 1993, the model gives a value of about 88 people, which is slightly more than the actual value of 87 people. 
D)  The display indicates that for the year 1995 , the model gives a value of about 88 people, which is slightly more than the actual value of 87 people. 
A)  The display indicates that for the year 1993, the model gives a value of about 87 people, which is slightly less than the actual value of 88 people. 
B)  The display indicates that for the year 1990, the model gives a value of 75.2 people, which is slightly more than the actual value of 75 people. 
C)  The display indicates that for the year 1993, the model gives a value of about 88 people, which is slightly more than the actual value of 87 people. 
D)  The display indicates that for the year 1995 , the model gives a value of about 88 people, which is slightly more than the actual value of 87 people.

Question 9

Write in exponential form.
-$\log _{6} 6^{-3}=-3$

Accepted Answer

A)  $3^{-6}=3^{-6}$ 
B)  $6^{-3}=3^{-6}$ 
C)  $6^{-3}=\log _{6} 3$ 
D)  $6^{-3}=6^{-3}$ 
A)  $3^{-6}=3^{-6}$ 
B)  $6^{-3}=3^{-6}$ 
C)  $6^{-3}=\log _{6} 3$ 
D)  $6^{-3}=6^{-3}$

Question 10

Graph the function.
-$f(x)=24 x-2$

Accepted Answer

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

Question 11

Find the logarithm. Give an approximation to four decimal places.
-$\log 2.52$

Accepted Answer

A)  0.4183 
B)  0.4014 
C)  0.3838 
D)  0.9243 
A)  0.4183 
B)  0.4014 
C)  0.3838 
D)  0.9243

Question 12

Evaluate the logarithm.
-$\log _{1 / 6} 1$

Accepted Answer

A)  2 
B)  -1 
C)  1 
D)  0 
A)  2 
B)  -1 
C)  1 
D)  0

Question 13

Write in exponential form.
-$\log _{3}(2 x-9)=3$

Accepted Answer

A)  $\{34\}$ 
B)  $\{3\}$ 
C)  $\{18\}$ 
D)  $\varnothing$ 
A)  $\{34\}$ 
B)  $\{3\}$ 
C)  $\{18\}$ 
D)  $\varnothing$

Question 14

Find the logarithm. Give an approximation to four decimal places
-$\log 0.0674$

Accepted Answer

A)  -1.1778 
B)  -2.6971 
C)  -1.1713 
D)  -1.1649 
A)  -1.1778 
B)  -2.6971 
C)  -1.1713 
D)  -1.1649

Question 15

The decibel level $D$ of a sound is related to its intensity $I$ by $D=10 \log \left(\frac{I}{I_{O}}\right)$. If $I_{O}$ is $10^{-12}$, then what is the intensity of a noise measured at 78 decibels? Express your answer in scientific notation, rounding to three significant digits, if necessary.

Accepted Answer

A)  $7.8 \times 10^{-10} \mathrm{watt} / \mathrm{m}^{2}$ 
B)  $2.44 \times 10^{15} \mathrm{watt} / \mathrm{m}^{2}$ 
C)  $6.31 \times 10^{-5} \mathrm{watt} / \mathrm{m}^{2}$ 
D)  $6.31 \times 10^{-4} \mathrm{watt} / \mathrm{m}^{2}$ 
A)  $7.8 \times 10^{-10} \mathrm{watt} / \mathrm{m}^{2}$ 
B)  $2.44 \times 10^{15} \mathrm{watt} / \mathrm{m}^{2}$ 
C)  $6.31 \times 10^{-5} \mathrm{watt} / \mathrm{m}^{2}$ 
D)  $6.31 \times 10^{-4} \mathrm{watt} / \mathrm{m}^{2}$

Question 16

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."
-$\{(-2,4),(2,-4),(8,-2),(-8,2)\}$

Accepted Answer

A)  $\{(4,-2),(-4,2),(-2,8),(2,-8)\}$ 
B)  $\{(4,-2),(-4,2),(-2,-8),(2,8)\}$ 
C)  Not one-to-one 
D)  $\{(4,-2),(-4,2),(8,-2),(2,-8)\}$ 
A)  $\{(4,-2),(-4,2),(-2,8),(2,-8)\}$ 
B)  $\{(4,-2),(-4,2),(-2,-8),(2,8)\}$ 
C)  Not one-to-one 
D)  $\{(4,-2),(-4,2),(8,-2),(2,-8)\}$

Question 17

Determine whether or not the function is one-to-one.
-The function that pairs the temperature in degrees Fahrenheit of a cup of coffee with its temperature in degrees Celsius.

Accepted Answer

A) True 
 B)False

Question 18

Find the logarithm. Give an approximation to four decimal places
-$\log 3857$

Accepted Answer

A)  3.5851 
B)  8.2576 
C)  3.5874 
D)  3.5862 
A)  3.5851 
B)  8.2576 
C)  3.5874 
D)  3.5862

Question 19

Evaluate the logarithm.
-$\log _{\sqrt{5}} \sqrt{5}$

Accepted Answer

A)  $-\frac{1}{2}$ 
B)  1 
C)  -2 
D)  -1 
A)  $-\frac{1}{2}$ 
B)  1 
C)  -2 
D)  -1

Question 20

Write in logarithmic form.
-$2^{0}=1$

Accepted Answer

A)  $\log _{2} 1=0$ 
B)  $\log _{2} 0=1$ 
C)  $\log _{0} 1=2$ 
D)  $\log _{1} 2=0$ 
A)  $\log _{2} 1=0$ 
B)  $\log _{2} 0=1$ 
C)  $\log _{0} 1=2$ 
D)  $\log _{1} 2=0$

Evaluate the logarithm. - $\log _{3} \sqrt{3}$

Write in exponential form. - $\log _{x}\left(\frac{81}{256}\right)=4$

Rewrite the given expression as a single logarithm. Assume that all variables are defined in such a way that variable expressions are positive and bases are positive numbers not equal to 1 . - $\log _{\mathrm{W}}\left(\mathrm{x}^{2}-16\right)-\log _{\mathrm{W}}(\mathrm{x}-4)$

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $\{(-6,8),(-19,8),(-7,-12)\}$

In your own words, explain what a logarithm is.

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $\{(9,-5),(13,6),(19,20)\}$

Solve the equation. Give the solution to three decimal places. - $9^{-\mathrm{x}-1}=71$

Write in exponential form. - $\log _{6} 6^{-3}=-3$

Graph the function. - $f(x)=24 x-2$

Find the logarithm. Give an approximation to four decimal places. - $\log 2.52$

Evaluate the logarithm. - $\log _{1 / 6} 1$

Write in exponential form. - $\log _{3}(2 x-9)=3$

Find the logarithm. Give an approximation to four decimal places - $\log 0.0674$

The decibel level $D$ of a sound is related to its intensity $I$ by $D=10 \log \left(\frac{I}{I_{O}}\right)$ . If $I_{O}$ is $10^{-12}$ , then what is the intensity of a noise measured at 78 decibels? Express your answer in scientific notation, rounding to three significant digits, if necessary.

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $\{(-2,4),(2,-4),(8,-2),(-8,2)\}$

Determine whether or not the function is one-to-one. -The function that pairs the temperature in degrees Fahrenheit of a cup of coffee with its temperature in degrees Celsius.

Find the logarithm. Give an approximation to four decimal places - $\log 3857$

Evaluate the logarithm. - $\log _{\sqrt{5}} \sqrt{5}$

Write in logarithmic form. - $2^{0}=1$

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Exam 10: Inverse, Exponential, and Logarithmic Functions

Evaluate the logarithm. - log⁡33\log _{3} \sqrt{3}log3​3​

Write in exponential form. - log⁡x(81256)=4\log _{x}\left(\frac{81}{256}\right)=4logx​(25681​)=4

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - {(−6,8),(−19,8),(−7,−12)}\{(-6,8),(-19,8),(-7,-12)\}{(−6,8),(−19,8),(−7,−12)}

In your own words, explain what a logarithm is.

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - {(9,−5),(13,6),(19,20)}\{(9,-5),(13,6),(19,20)\}{(9,−5),(13,6),(19,20)}

Solve the equation. Give the solution to three decimal places. - 9−x−1=719^{-\mathrm{x}-1}=719−x−1=71

Write in exponential form. - log⁡66−3=−3\log _{6} 6^{-3}=-3log6​6−3=−3

Graph the function. - f(x)=24x−2f(x)=24 x-2f(x)=24x−2

Find the logarithm. Give an approximation to four decimal places. - log⁡2.52\log 2.52log2.52

Evaluate the logarithm. - log⁡1/61\log _{1 / 6} 1log1/6​1

Write in exponential form. - log⁡3(2x−9)=3\log _{3}(2 x-9)=3log3​(2x−9)=3

Find the logarithm. Give an approximation to four decimal places - log⁡0.0674\log 0.0674log0.0674

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - {(−2,4),(2,−4),(8,−2),(−8,2)}\{(-2,4),(2,-4),(8,-2),(-8,2)\}{(−2,4),(2,−4),(8,−2),(−8,2)}

Determine whether or not the function is one-to-one. -The function that pairs the temperature in degrees Fahrenheit of a cup of coffee with its temperature in degrees Celsius.

Find the logarithm. Give an approximation to four decimal places - log⁡3857\log 3857log3857

Evaluate the logarithm. - log⁡55\log _{\sqrt{5}} \sqrt{5}log5​​5​

Write in logarithmic form. - 20=12^{0}=120=1

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Evaluate the logarithm. - $\log _{3} \sqrt{3}$

Write in exponential form. - $\log _{x}\left(\frac{81}{256}\right)=4$

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $\{(-6,8),(-19,8),(-7,-12)\}$

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $\{(9,-5),(13,6),(19,20)\}$

Solve the equation. Give the solution to three decimal places. - $9^{-\mathrm{x}-1}=71$

Write in exponential form. - $\log _{6} 6^{-3}=-3$

Graph the function. - $f(x)=24 x-2$

Find the logarithm. Give an approximation to four decimal places. - $\log 2.52$

Evaluate the logarithm. - $\log _{1 / 6} 1$

Write in exponential form. - $\log _{3}(2 x-9)=3$

Find the logarithm. Give an approximation to four decimal places - $\log 0.0674$

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $\{(-2,4),(2,-4),(8,-2),(-8,2)\}$

Find the logarithm. Give an approximation to four decimal places - $\log 3857$

Evaluate the logarithm. - $\log _{\sqrt{5}} \sqrt{5}$

Write in logarithmic form. - $2^{0}=1$