Question 1

Use the change of base rule to find the logarithm to four decimal places.
-$$\log _ { 6 } 61.70$$

Accepted Answer

A)  0.4347 
B)  1.7903 
C)  2.3007 
D)  10.2833 
A)  0.4347 
B)  1.7903 
C)  2.3007 
D)  10.2833

Question 2

Graph the function. Give the domain and range.
-$$f ( x ) = \log _ { 4 } ( x - 1 )$$

Accepted Answer

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

Question 3

Solve the equation.
-$2401 ^ { x } = 7$

Accepted Answer

A)  $\{ 4 \}$ 
B)  $\left\{ \frac { 1 } { 4 } \right\}$ 
C)  $\{ - 4 \}$ 
D)  $\left\{ - \frac { 1 } { 4 } \right\}$ 
A)  $\{ 4 \}$ 
B)  $\left\{ \frac { 1 } { 4 } \right\}$ 
C)  $\{ - 4 \}$ 
D)  $\left\{ - \frac { 1 } { 4 } \right\}$

Question 4

Graph the function.
-$f(x)=\left(\frac{2}{5}\right)^{x}$

Accepted Answer

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

Question 5

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 $\ln \frac { a ^ { 6 } } { b ^ { 2 } }$

Accepted Answer

A)  $6 u + 2 v$ 
B)  $6 u - 2 v$ 
C)  $2 u - 6 v$ 
D)  $u ^ { 6 } - v ^ { 2 }$ n ln.285) 
A)  $6 u + 2 v$ 
B)  $6 u - 2 v$ 
C)  $2 u - 6 v$ 
D)  $u ^ { 6 } - v ^ { 2 }$ n ln.285)

Question 6

For the function as defined that is one-to-one, graph f and $$\mathbf { f } ^ { - 1 }$$ on the same axes.
-$f(x)=\sqrt{x+5}$

Accepted Answer

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

Question 7

Choose the one alternative that best completes the statement or answers the question.
-A lake is stocked with 437 fish of a new variety. The size of the lake, the availability of food, and the number of other fish restrict growth in the lake to a limiting value of 2731 . The population of fish in the lake after time $\mathrm { t }$, in months, is given by the function $\mathrm { P } ( \mathrm { t } ) = \frac { 2731 } { 1 + 4.4 \mathrm { e } ^ { - 0.25 \mathrm { t } } }$. Find the population after 15 months.

Accepted Answer

A)  2485 fish 
B)  2475 fish 
C)  2490 fish 
D)  2465 fish 
A)  2485 fish 
B)  2475 fish 
C)  2490 fish 
D)  2465 fish

Question 8

Choose the one alternative that best completes the statement or answers the question.
-The purchasing power of a dollar is decreasing at the rate of $2.8 \%$ annually, compounded continuously. How long will it take for the purchasing power of $\$ 1.00$ to be worth $\$ 0.33$ ? Round answers to the nearest hundredth.

Accepted Answer

A)  $0.40 \mathrm { yr }$ 
B)  $11.79 \mathrm { yr }$ 
C)  $3.96 \mathrm { yr }$ 
D)  $39.60 \mathrm { yr }$ 
A)  $0.40 \mathrm { yr }$ 
B)  $11.79 \mathrm { yr }$ 
C)  $3.96 \mathrm { yr }$ 
D)  $39.60 \mathrm { yr }$

Question 9

Write in logarithmic form.
-$$\left( \frac { 3 } { 10 } \right) ^ { - 2 } = \frac { 100 } { 9 }$$

Accepted Answer

A)  $\log _ { 3 / 10 } \left( \frac { 100 } { 9 } \right) = - 2$ 
B)  $\log _ { 2 } \frac { 3 } { 10 } = \frac { 3 ^ { - 2 } } { 10 ^ { - 2 } }$ 
C)  $\frac { \log _ { 2 } 3 ^ { - 2 } } { \log _ { 2 } 10 ^ { - 2 } } = \frac { 10 } { 3 }$ 
D)  $\log _ { - 2 } \left( \frac { 10 ^ { - 2 } } { 3 ^ { - 2 } } \right) = \frac { 10 } { 3 }$ 
A)  $\log _ { 3 / 10 } \left( \frac { 100 } { 9 } \right) = - 2$ 
B)  $\log _ { 2 } \frac { 3 } { 10 } = \frac { 3 ^ { - 2 } } { 10 ^ { - 2 } }$ 
C)  $\frac { \log _ { 2 } 3 ^ { - 2 } } { \log _ { 2 } 10 ^ { - 2 } } = \frac { 10 } { 3 }$ 
D)  $\log _ { - 2 } \left( \frac { 10 ^ { - 2 } } { 3 ^ { - 2 } } \right) = \frac { 10 } { 3 }$

Question 10

Find the value. Give an approximation to four decimal places.
-$\ln \left( 6.9 \times e ^ { - 6 } \right)$

Accepted Answer

A)  $- 4.0685$ 
B)  $1.9319$ 
C)  $1.9315$ 
D)  $7.9315$ 
A)  $- 4.0685$ 
B)  $1.9319$ 
C)  $1.9315$ 
D)  $7.9315$

Question 11

The graph of a function f is given. Use the graph to find the indicated value.
-Let f(x) compute the cost of a rental car after x days of use at $50 per day. What is the interpretation of the solution of $f ^ { - 1 } ( x )$ = 184?

Accepted Answer

A)  The cost of rental for 50 days 
B)  The number of days rented for $184 
C)  The cost of rental for 184 days 
D)  The number of days rented for $50 
A)  The cost of rental for 50 days 
B)  The number of days rented for $184 
C)  The cost of rental for 184 days 
D)  The number of days rented for $50

Question 12

Write an equivalent expression in exponential form.
-$$\log _ { x } 49 = - 2$$

Accepted Answer

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

Question 13

Choose the one alternative that best completes the statement or answers the question.
-In the formula $\mathrm { A } ( \mathrm { t } ) = \mathrm { A } _ { 0 } \mathrm { e } ^ { \mathrm { kt } } , \mathrm { A }$ is the amount of radioactive material remaining from an initial amount $\mathrm { A } _ { 0 }$ at a given time $\mathrm { t }$, and $\mathrm { k }$ is a negative constant determined by the nature of the material A certain radioactive isotope decays at a rate of $0.25 \%$ annually. Determine the half-life of this isotope, to the nearest year.

Accepted Answer

A)  $3 \mathrm { yr }$ 
B)  $277 \mathrm { yr }$ 
C)  $120 \mathrm { yr }$ 
D)  $200 \mathrm { yr }$ 
A)  $3 \mathrm { yr }$ 
B)  $277 \mathrm { yr }$ 
C)  $120 \mathrm { yr }$ 
D)  $200 \mathrm { yr }$

Question 14

Find the future value.
-$2126.13 invested for 11 years at 3% compounded monthly

Accepted Answer

A)  $2956.16 
B)  $2953.74 
C)  $2950.14 
D)  $2943.06 
A)  $2956.16 
B)  $2953.74 
C)  $2950.14 
D)  $2943.06

Question 15

Choose the one alternative that best completes the statement or answers the question.
-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)  704 
B)  240 
C)  470 
D)  74 
A)  704 
B)  240 
C)  470 
D)  74

Question 16

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

Accepted Answer

A)  $w = \frac { 3 \cdot \ln ( 1 - a ) } { I t P }$ 
B)  $w = - \frac { 3 } { a } \ln \left( 1 - \frac { \mathrm { IP } } { \mathrm { t } } \right)$ 
C)  w $= \frac { \mathrm { ItP } \cdot \ln ( 1 - \mathrm { a } ) } { 3 }$ 
D)  $w = - \frac { 3 \ln ( 1 - \mathrm { IPt } ) } { \mathrm { a } }$ 
A)  $w = \frac { 3 \cdot \ln ( 1 - a ) } { I t P }$ 
B)  $w = - \frac { 3 } { a } \ln \left( 1 - \frac { \mathrm { IP } } { \mathrm { t } } \right)$ 
C)  w $= \frac { \mathrm { ItP } \cdot \ln ( 1 - \mathrm { a } ) } { 3 }$ 
D)  $w = - \frac { 3 \ln ( 1 - \mathrm { IPt } ) } { \mathrm { a } }$

Question 17

Solve the problem.
-Suppose $f ( x ) = 33.8 + 1.5 \log ( x + 1 )$ models salinity of ocean water to depths of 1000 meters at a certain latitude. $x$ is the depth in meters and $f ( x )$ is in grams of salt per kilogram of seawater. Approximate the salinity (to the nearest hundredth) when the depth is 897 meters.

Accepted Answer

A)  $- 29.37 \mathrm {~g} / \mathrm { kg }$ 
B)  $98.32 \mathrm {~g} / \mathrm { kg }$ 
C)  $38.23 \mathrm {~g} / \mathrm { kg }$ 
D)  $101.32 \mathrm {~g} / \mathrm { kg }$ 
A)  $- 29.37 \mathrm {~g} / \mathrm { kg }$ 
B)  $98.32 \mathrm {~g} / \mathrm { kg }$ 
C)  $38.23 \mathrm {~g} / \mathrm { kg }$ 
D)  $101.32 \mathrm {~g} / \mathrm { kg }$

Question 18

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth.
-$$3 ^ { x } = 19$$

Accepted Answer

A)  $\{ 6.33 \}$ 
B)  $\{ 0.37 \}$ 
C)  $\{ 1.85 \}$ 
D)  $\{ 2.68 \}$ 
A)  $\{ 6.33 \}$ 
B)  $\{ 0.37 \}$ 
C)  $\{ 1.85 \}$ 
D)  $\{ 2.68 \}$

Question 19

Write an equivalent expression in exponential form.
-$$x = \log _ { 6 } \sqrt [ 5 ] { 216 }$$

Accepted Answer

A)  $\left\{ - \frac { 3 } { 5 } \right\}$ 
B)  $\left\{ \frac { 3 } { 5 } \right\}$ 
C)  $\left\{ \frac { 5 } { 3 } \right\}$ 
D)  $\{ 15 \}$ 
A)  $\left\{ - \frac { 3 } { 5 } \right\}$ 
B)  $\left\{ \frac { 3 } { 5 } \right\}$ 
C)  $\left\{ \frac { 5 } { 3 } \right\}$ 
D)  $\{ 15 \}$

Question 20

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth.
-$$e ^ { x } = 7$$

Accepted Answer

A)  $\{ 1.95 \}$ 
B)  $\{ 198.25 \}$ 
C)  $\{ 0.85 \}$ 
D)  $\{ 1096.63 \}$ 
A)  $\{ 1.95 \}$ 
B)  $\{ 198.25 \}$ 
C)  $\{ 0.85 \}$ 
D)  $\{ 1096.63 \}$

Use the change of base rule to find the logarithm to four decimal places. - $\log _ { 6 } 61.70$

Graph the function. Give the domain and range. - $f ( x ) = \log _ { 4 } ( x - 1 )$ $Graph the function. Give the domain and range. - f ( x ) = \log _ { 4 } ( x - 1 )$

Solve the equation. - $2401 ^ { x } = 7$

Graph the function. - $f(x)=\left(\frac{2}{5}\right)^{x}$ $Graph the function. - f(x)=\left(\frac{2}{5}\right)^{x}$

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 $\ln \frac { a ^ { 6 } } { b ^ { 2 } }$

For the function as defined that is one-to-one, graph f and $\mathbf { f } ^ { - 1 }$ on the same axes. - $f(x)=\sqrt{x+5}$ $For the function as defined that is one-to-one, graph f and \mathbf { f } ^ { - 1 } on the same axes. - f(x)=\sqrt{x+5}$

Write in logarithmic form. - $\left( \frac { 3 } { 10 } \right) ^ { - 2 } = \frac { 100 } { 9 }$

Find the value. Give an approximation to four decimal places. - $\ln \left( 6.9 \times e ^ { - 6 } \right)$

The graph of a function f is given. Use the graph to find the indicated value. -Let f(x) compute the cost of a rental car after x days of use at $50 per day. What is the interpretation of the solution of $f ^ { - 1 } ( x )$ = 184?

Write an equivalent expression in exponential form. - $\log _ { x } 49 = - 2$

Find the future value. -$2126.13 invested for 11 years at 3% compounded monthly

Choose the one alternative that best completes the statement or answers the question. -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 for the indicated variable. - $I = \frac { t } { P } \left( 1 - e ^ { - a w / 3 } \right)$ , for $w$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $3 ^ { x } = 19$

Write an equivalent expression in exponential form. - $x = \log _ { 6 } \sqrt [ 5 ] { 216 }$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $e ^ { x } = 7$

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

Use the change of base rule to find the logarithm to four decimal places. - log⁡661.70\log _ { 6 } 61.70log6​61.70

Graph the function. Give the domain and range. - f(x)=log⁡4(x−1)f ( x ) = \log _ { 4 } ( x - 1 )f(x)=log4​(x−1)

Solve the equation. - 2401x=72401 ^ { x } = 72401x=7

Graph the function. - f(x)=(25)xf(x)=\left(\frac{2}{5}\right)^{x}f(x)=(52​)x

For the function as defined that is one-to-one, graph f and f−1\mathbf { f } ^ { - 1 }f−1 on the same axes. - f(x)=x+5f(x)=\sqrt{x+5}f(x)=x+5​

Write in logarithmic form. - (310)−2=1009\left( \frac { 3 } { 10 } \right) ^ { - 2 } = \frac { 100 } { 9 }(103​)−2=9100​

Find the value. Give an approximation to four decimal places. - ln⁡(6.9×e−6)\ln \left( 6.9 \times e ^ { - 6 } \right)ln(6.9×e−6)

The graph of a function f is given. Use the graph to find the indicated value. -Let f(x) compute the cost of a rental car after x days of use at $50 per day. What is the interpretation of the solution of f−1(x)f ^ { - 1 } ( x )f−1(x) = 184?

Write an equivalent expression in exponential form. - log⁡x49=−2\log _ { x } 49 = - 2logx​49=−2