Question 1

Write in exponential form.
-$\log _{8} x=\frac{2}{3}$

Accepted Answer

A)  $\{4\}$ 
B)  $\{2\}$ 
C)  $\{8\}$ 
D)  $\left\{\frac{16}{3}\right\}$ 
A)  $\{4\}$ 
B)  $\{2\}$ 
C)  $\{8\}$ 
D)  $\left\{\frac{16}{3}\right\}$

Question 2

Write in exponential form.
-$\log _{2} 8=3$

Accepted Answer

A)  $2^{3}=8$ 
B)  $8^{3}=2$ 
C)  $3^{2}=8$ 
D)  $2^{8}=3$ 
A)  $2^{3}=8$ 
B)  $8^{3}=2$ 
C)  $3^{2}=8$ 
D)  $2^{8}=3$

Question 3

Express as a product.
-$\log _{10} \sqrt[6]{5}$

Accepted Answer

A)  $\log _{60} 5$ 
B)  $10 \log _{6} 5$ 
C)  $\frac{1}{6} \log _{10} 5^{6}$ 
D)  $\frac{1}{6} \log _{10} 5$ 
A)  $\log _{60} 5$ 
B)  $10 \log _{6} 5$ 
C)  $\frac{1}{6} \log _{10} 5^{6}$ 
D)  $\frac{1}{6} \log _{10} 5$

Question 4

Use the formula $\mathrm{N}=\mathrm{Ie}^{\mathrm{kt}}$, where $\mathrm{N}$ is the population at time $\mathrm{t}$, $\mathrm{I}$ is the initial population, and $\mathrm{k}$ is a growth constant equal to the percent of growth (expressed in decimal form) per unit of time. How long will it take for the population of a certain country to double if its annual growth rate is $7.8 \%$ ? Round your answer to the nearest year.

Accepted Answer

A)  $4 \mathrm{yr}$ 
B)  $1 \mathrm{yr}$ 
C)  $9 \mathrm{yr}$ 
D)  $26 \mathrm{yr}$ 
A)  $4 \mathrm{yr}$ 
B)  $1 \mathrm{yr}$ 
C)  $9 \mathrm{yr}$ 
D)  $26 \mathrm{yr}$

Question 5

When solving an exponential equation using logarithms, when is it easier to use common logarithms?

Accepted Answer

When the b

Question 6

An accountant tabulated a firm's profits for four recent years in the following table:
 
The accountant then fit both a linear graph and an exponential curve (seen below) to the data, in order to estimate future profits. Use the exponential graph to estimate the profits in the year 2002.

Accepted Answer

A)  About $\$ 1,000,000$ 
B)  About $\$ 750,000$ 
C)  About \$1,300,000 
D)  About $\$ 1,700,000$ 
A)  About $\$ 1,000,000$ 
B)  About $\$ 750,000$ 
C)  About \$1,300,000 
D)  About $\$ 1,700,000$

Question 7

The number of visitors to a tourist attraction (for the first few years after its opening) can be approximated by $\mathrm{V}(\mathrm{x})=50+10 \log _{2} \mathrm{x}$, where $\mathrm{x}$ represents the number of month after the opening of the attraction. Find the number of visitors 32 months after the opening of the attraction.

Accepted Answer

A)  82 visitors 
B)  55 visitors 
C)  370 visitors 
D)  100 visitors 
A)  82 visitors 
B)  55 visitors 
C)  370 visitors 
D)  100 visitors

Question 8

$\log _{19} 16-\log _{16} 19=0$

Accepted Answer

A) True 
 B)False

Question 9

Determine whether or not the function is one-to-one.
-$f(x)=\sqrt{4-x^{2}}$

Accepted Answer

A) True 
 B)False

Question 10

The function $\mathrm{A}=\mathrm{A}_{0} \mathrm{e}^{-0.00693 \mathrm{x}}$ models the amount in pounds of a particular radioactive material stored in a concrete vault, where $\mathrm{x}$ is the number of years since the material was put into the vault. If 500 pounds of the material are placed in the vault, how much time will need to pass for only 268 pounds to remain?

Accepted Answer

A)  $95 \mathrm{yr}$ 
B)  $90 \mathrm{yr}$ 
C)  $100 \mathrm{yr}$ 
D)  $180 \mathrm{yr}$ 
A)  $95 \mathrm{yr}$ 
B)  $90 \mathrm{yr}$ 
C)  $100 \mathrm{yr}$ 
D)  $180 \mathrm{yr}$

Question 11

Determine whether or not the function is one-to-one.
-This chart shows the number of hits for five Little League baseball teams.

Accepted Answer

A) True 
 B)False

Question 12

Evaluate the given logarithm by applying the appropriate rule(s). DO NOT USE A CALCULATOR.
-Given $\log _{10} 2=0.3010$ and $\log _{10} 3=0.4771$, evaluate $\log _{10} 6$.

Accepted Answer

A)  0.7781 
B)  0.9030 
C)  0.1436 
D)  0.9542 
A)  0.7781 
B)  0.9030 
C)  0.1436 
D)  0.9542

Question 13

Wind speed varies in the first twenty meters above the ground. For a particular day, let $f(x)=1.4 \ln x+9.0$ compute the wind speed $x$ meters above the ground. What is the wind speed 11 meters above the ground? Round your result to the nearest hundredth.

Accepted Answer

A)  -5.64 meters per second 
B)  11.40 meters per second 
C)  12.08 meters per second 
D)  12.36 meters per second 
A)  -5.64 meters per second 
B)  11.40 meters per second 
C)  12.08 meters per second 
D)  12.36 meters per second

Question 14

A computer is purchased for $\$ 3200$. Its value each year is about $77 \%$ of the value the preceding year. Its value, in dollars, after $t$ years is given by the exponential function $V(t)=3200(0.77)^{t}$. Find the value of the computer after 4 years.

Accepted Answer

A)  $\$ 9856.00$ 
B)  $\$ 866.17$ 
C)  $\$ 1124.90$ 
D)  $\$ 666.95$ 
A)  $\$ 9856.00$ 
B)  $\$ 866.17$ 
C)  $\$ 1124.90$ 
D)  $\$ 666.95$

Question 15

Determine whether or not the function is one-to-one.
-This chart shows the number of living relatives in five families.

Accepted Answer

A) True 
 B)False

Question 16

Express as a product.
-$\log _{b} 3^{3}$

Accepted Answer

A)  $b \log _{30} 3^{3}$ 
B)  $b \log _{3} 3$ 
C)  $3 \log _{b} 3^{3}$ 
D)  $3 \log _{b} 3$ 
A)  $b \log _{30} 3^{3}$ 
B)  $b \log _{3} 3$ 
C)  $3 \log _{b} 3^{3}$ 
D)  $3 \log _{b} 3$

Question 17

Graph the inverse of $f$, given the graph of $f$ below.
-

Accepted Answer

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

Question 18

The number of bacteria growing in an incubation culture increases with time according to $B(x)=6700(2)^{x}$, where $x$ is time in days. Find the number of bacteria when $x=0$.

Accepted Answer

A)  26,800 
B)  13,400 
C)  40,200 
D)  6700 
A)  26,800 
B)  13,400 
C)  40,200 
D)  6700

Question 19

Solve the equation. Use natural logarithms. When appropriate, give solutions to three decimal places unless otherwise indicated.
-$\mathrm{e}^{\ln 3 x}=\mathrm{e}^{\ln (2 x+4)}$

Accepted Answer

A)  $\{4\}$ 
B)  $\{-4\}$ 
C)  $\left\{-\frac{4}{5}\right\}$ 
D)  $\left\{\frac{4}{5}\right\}$ 
A)  $\{4\}$ 
B)  $\{-4\}$ 
C)  $\left\{-\frac{4}{5}\right\}$ 
D)  $\left\{\frac{4}{5}\right\}$

Question 20

Determine whether or not the function is one-to-one.
-The function that pairs the radius of a spherical bowling ball with its volume.

Accepted Answer

A) True 
 B)False

Write in exponential form. - $\log _{8} x=\frac{2}{3}$

Write in exponential form. - $\log _{2} 8=3$

Express as a product. - $\log _{10} \sqrt[6]{5}$

When solving an exponential equation using logarithms, when is it easier to use common logarithms?

An accountant tabulated a firm's profits for four recent years in the following table: The accountant then fit both a linear graph and an exponential curve (seen below) to the data, in order to estimate future profits. Use the exponential graph to estimate the profits in the year 2002.

$\log _{19} 16-\log _{16} 19=0$

Determine whether or not the function is one-to-one. - $f(x)=\sqrt{4-x^{2}}$

Determine whether or not the function is one-to-one. -This chart shows the number of hits for five Little League baseball teams.

Evaluate the given logarithm by applying the appropriate rule(s). DO NOT USE A CALCULATOR. -Given $\log _{10} 2=0.3010$ and $\log _{10} 3=0.4771$ , evaluate $\log _{10} 6$ .

Wind speed varies in the first twenty meters above the ground. For a particular day, let $f(x)=1.4 \ln x+9.0$ compute the wind speed $x$ meters above the ground. What is the wind speed 11 meters above the ground? Round your result to the nearest hundredth.

A computer is purchased for $\$ 3200$ . Its value each year is about $77 \%$ of the value the preceding year. Its value, in dollars, after $t$ years is given by the exponential function $V(t)=3200(0.77)^{t}$ . Find the value of the computer after 4 years.

Determine whether or not the function is one-to-one. -This chart shows the number of living relatives in five families.

Express as a product. - $\log _{b} 3^{3}$

Graph the inverse of $f$ , given the graph of $f$ below. -

The number of bacteria growing in an incubation culture increases with time according to $B(x)=6700(2)^{x}$ , where $x$ is time in days. Find the number of bacteria when $x=0$ .

Solve the equation. Use natural logarithms. When appropriate, give solutions to three decimal places unless otherwise indicated. - $\mathrm{e}^{\ln 3 x}=\mathrm{e}^{\ln (2 x+4)}$

Determine whether or not the function is one-to-one. -The function that pairs the radius of a spherical bowling ball with its volume.

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

Write in exponential form. - log⁡8x=23\log _{8} x=\frac{2}{3}log8​x=32​

Write in exponential form. - log⁡28=3\log _{2} 8=3log2​8=3

Express as a product. - log⁡1056\log _{10} \sqrt[6]{5}log10​65​

When solving an exponential equation using logarithms, when is it easier to use common logarithms?

An accountant tabulated a firm's profits for four recent years in the following table: The accountant then fit both a linear graph and an exponential curve (seen below) to the data, in order to estimate future profits. Use the exponential graph to estimate the profits in the year 2002.

log⁡1916−log⁡1619=0\log _{19} 16-\log _{16} 19=0log19​16−log16​19=0

Determine whether or not the function is one-to-one. - f(x)=4−x2f(x)=\sqrt{4-x^{2}}f(x)=4−x2​

Determine whether or not the function is one-to-one. -This chart shows the number of hits for five Little League baseball teams.

Evaluate the given logarithm by applying the appropriate rule(s). DO NOT USE A CALCULATOR. -Given log⁡102=0.3010\log _{10} 2=0.3010log10​2=0.3010 and log⁡103=0.4771\log _{10} 3=0.4771log10​3=0.4771 , evaluate log⁡106\log _{10} 6log10​6 .

Wind speed varies in the first twenty meters above the ground. For a particular day, let f(x)=1.4ln⁡x+9.0f(x)=1.4 \ln x+9.0f(x)=1.4lnx+9.0 compute the wind speed xxx meters above the ground. What is the wind speed 11 meters above the ground? Round your result to the nearest hundredth.

A computer is purchased for $3200\$ 3200$3200 . Its value each year is about 77%77 \%77% of the value the preceding year. Its value, in dollars, after ttt years is given by the exponential function V(t)=3200(0.77)tV(t)=3200(0.77)^{t}V(t)=3200(0.77)t . Find the value of the computer after 4 years.

Determine whether or not the function is one-to-one. -This chart shows the number of living relatives in five families.

Express as a product. - log⁡b33\log _{b} 3^{3}logb​33

Graph the inverse of fff , given the graph of fff below. -

The number of bacteria growing in an incubation culture increases with time according to B(x)=6700(2)xB(x)=6700(2)^{x}B(x)=6700(2)x , where xxx is time in days. Find the number of bacteria when x=0x=0x=0 .

Solve the equation. Use natural logarithms. When appropriate, give solutions to three decimal places unless otherwise indicated. - eln⁡3x=eln⁡(2x+4)\mathrm{e}^{\ln 3 x}=\mathrm{e}^{\ln (2 x+4)}eln3x=eln(2x+4)

Determine whether or not the function is one-to-one. -The function that pairs the radius of a spherical bowling ball with its volume.

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

Write in exponential form. - $\log _{8} x=\frac{2}{3}$

Write in exponential form. - $\log _{2} 8=3$

Express as a product. - $\log _{10} \sqrt[6]{5}$

$\log _{19} 16-\log _{16} 19=0$

Determine whether or not the function is one-to-one. - $f(x)=\sqrt{4-x^{2}}$

Evaluate the given logarithm by applying the appropriate rule(s). DO NOT USE A CALCULATOR. -Given $\log _{10} 2=0.3010$ and $\log _{10} 3=0.4771$ , evaluate $\log _{10} 6$ .

Wind speed varies in the first twenty meters above the ground. For a particular day, let $f(x)=1.4 \ln x+9.0$ compute the wind speed $x$ meters above the ground. What is the wind speed 11 meters above the ground? Round your result to the nearest hundredth.

A computer is purchased for $\$ 3200$ . Its value each year is about $77 \%$ of the value the preceding year. Its value, in dollars, after $t$ years is given by the exponential function $V(t)=3200(0.77)^{t}$ . Find the value of the computer after 4 years.

Express as a product. - $\log _{b} 3^{3}$

Graph the inverse of $f$ , given the graph of $f$ below. -

The number of bacteria growing in an incubation culture increases with time according to $B(x)=6700(2)^{x}$ , where $x$ is time in days. Find the number of bacteria when $x=0$ .

Solve the equation. Use natural logarithms. When appropriate, give solutions to three decimal places unless otherwise indicated. - $\mathrm{e}^{\ln 3 x}=\mathrm{e}^{\ln (2 x+4)}$