Question 1

Graph the function.
-$f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { - x }$

Accepted Answer

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

Question 2

Write the equation in logarithmic form.
-$5 ^ { 2 } = 25$

Accepted Answer

A)  $\log _ { 2 } 25 = 5$ 
B)  $\log _ { 5 } 25 = 2$ 
C)  $\log _ { 5 } 2 = 25$ 
D)  $\log _ { 25 } 5 = 2$ 
A)  $\log _ { 2 } 25 = 5$ 
B)  $\log _ { 5 } 25 = 2$ 
C)  $\log _ { 5 } 2 = 25$ 
D)  $\log _ { 25 } 5 = 2$

Question 3

Find the number N. Round N to six decimal places.
-log N = -1.4263

Accepted Answer

A) 0.037471 
B) 0.720062 
C) 26.687015 
D) 4.163267 
A) 0.037471 
B) 0.720062 
C) 26.687015 
D) 4.163267

Question 4

Evaluate.
-$$7 \left( 10 ^ { \log 2.9 } \right)$$

Accepted Answer

A) 20.3 
B) 7.4530 
C) 2.03 
D) 203 
A) 20.3 
B) 7.4530 
C) 2.03 
D) 203

Question 5

Find the value obtained when 10 is raised to the given exponent. Round to three significant digits.
--0.8514

Accepted Answer

A) 7.10 
B) 0.141 
C) -0.141 
D) -7.10 
A) 7.10 
B) 0.141 
C) -0.141 
D) -7.10

Question 6

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function.
-f(x)= 4x

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - 4 \mathrm { x }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 4 }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 4 } { \mathrm { x } }$ 
D) not a one-to-one function 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - 4 \mathrm { x }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 4 }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 4 } { \mathrm { x } }$ 
D) not a one-to-one function

Question 7

Write the equation in logarithmic form.
-$343 ^ { 1 / 3 } = 7$

Accepted Answer

A)  $\log _ { 343 } \frac { 1 } { 3 } = 7$ 
B)  $\log _ { 7 } \frac { 1 } { 3 } = 343$ 
C)  $\log _ { 343 } 7 = \frac { 1 } { 3 }$ 
D)  $\log _ { 3 } 343 = 7$ 
A)  $\log _ { 343 } \frac { 1 } { 3 } = 7$ 
B)  $\log _ { 7 } \frac { 1 } { 3 } = 343$ 
C)  $\log _ { 343 } 7 = \frac { 1 } { 3 }$ 
D)  $\log _ { 3 } 343 = 7$

Question 8

Solve the problem.
-The pH of a solution ranges from 0 to 14. An acid has a pH less than 7. Pure water is neutral and has a pH of 7. The pH of a solution is given by pH = - log x where x represents the concentration of the hydrogen ions in the
Solution in moles per liter. Find the hydrogen ion concentration if thehe $\mathrm { pH } = 2$

Accepted Answer

A)  $10 ^ { - 2 }$ 
B) 0.69 
C) 0.5 
D)  $10^2$ 
A)  $10 ^ { - 2 }$ 
B) 0.69 
C) 0.5 
D)  $10^2$

Question 9

For the given functions f and g , find the indicated value.
-$$\begin{array} { l } 
f ( x ) = 2 x + 4 , \quad g ( x ) = 4 x ^ { 2 } + 1 \
( g \circ f ) ( 1 )
\end{array}$$

Accepted Answer

A) 145 
B) 101 
C) 16 
D) 14 
A) 145 
B) 101 
C) 16 
D) 14

Question 10

Write the equation in logarithmic form.
-$$10 ^ { 0.6931 } = 2$$

Accepted Answer

A)  $\log _ { 0.6931 } 10 = 2$ 
B)  $\log _ { 10 } 2 = 0.6931$ 
C)  $\log _ { 10 } 0.6931 = 2$ 
D)  $\log_{ 0.6931}2 = 10$ 
A)  $\log _ { 0.6931 } 10 = 2$ 
B)  $\log _ { 10 } 2 = 0.6931$ 
C)  $\log _ { 10 } 0.6931 = 2$ 
D)  $\log_{ 0.6931}2 = 10$

Question 11

Determine whether the given functions are inverses of each other.
-$$f ( x ) = x ^ { 4 } - 19 , \quad g ( x ) = \sqrt [ 4 ] { x - 19 }$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 12

By changing the logarithm to exponential form, evaluate the common logarithm without the use of a calculator.
-log 0.0001

Accepted Answer

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

Question 13

Solve the problem.
-The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential
Growth model A $\mathrm { A } = 5200 \mathrm { e } ^ { 0.06 t }$ . By what perce. By what percntage is the account increasing each year?

Accepted Answer

A) 6.7% 
B) 6.2% 
C) 6.4% 
D) 6.6% 
A) 6.7% 
B) 6.2% 
C) 6.4% 
D) 6.6%

Question 14

Determine whether the function is a one-to-one function.
-$$\{ ( - 5,2 ) , ( - 4,2 ) , ( - 3,6 ) , ( - 2 , - 6 ) \}$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 15

Use properties of logarithms to expand the logarithmic expression as much as possible.
-$$\log _ { 17 } \frac { 16 \sqrt { \mathrm { r } } } { \mathrm { s } }$$

Accepted Answer

A)  $\log _ { 17 } \mathrm {~s} - \log _ { 17 } 16 - \frac { 1 } { 2 } \log _ { 17 } \mathrm { r }$ 
B)  $\log _ { 17 } 16 \cdot \frac { 1 } { 2 } \log _ { 17 } \mathrm {~m} \div \log _ { 17 } \mathrm {~s}$ 
C)  $\log _ { 17 } ( 16 \sqrt { r } ) - \log _ { 17 } \mathrm {~s}$ 
D)  $\log _ { 17 } 16 + \frac { 1 } { 2 } \log _ { 17 } \mathrm { r } - \log _ { 17 } \mathrm {~s}$ 
A)  $\log _ { 17 } \mathrm {~s} - \log _ { 17 } 16 - \frac { 1 } { 2 } \log _ { 17 } \mathrm { r }$ 
B)  $\log _ { 17 } 16 \cdot \frac { 1 } { 2 } \log _ { 17 } \mathrm {~m} \div \log _ { 17 } \mathrm {~s}$ 
C)  $\log _ { 17 } ( 16 \sqrt { r } ) - \log _ { 17 } \mathrm {~s}$ 
D)  $\log _ { 17 } 16 + \frac { 1 } { 2 } \log _ { 17 } \mathrm { r } - \log _ { 17 } \mathrm {~s}$

Question 16

Find the common logarithm of the number. Round answer to four decimal places.
-log 3447

Accepted Answer

A) 3.5362 
B) 3.5374 
C) 3.5387 
D) 8.1453 
A) 3.5362 
B) 3.5374 
C) 3.5387 
D) 8.1453

Question 17

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth.
-$$\log _ { 3 } x ^ { 2 } = \log _ { 3 } ( 2 x + 8 )$$

Accepted Answer

A)  $\frac { 4 } { 3 }$ 
B) 4 
C) 4, -2 
D) no solution 
A)  $\frac { 4 } { 3 }$ 
B) 4 
C) 4, -2 
D) no solution

Question 18

Find the unknown value.
-$\log _ { 9 } \frac { 1 } { 81 } = y$

Accepted Answer

A) -2 
B) 9 
C) -9 
D) 2 
A) -2 
B) 9 
C) -9 
D) 2

Question 19

Determine whether the function is a one-to-one function.
-$$y = - x ^ { 2 } + 3$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 20

Find the antilog of the logarithm. Round the answer to six decimal places.
--0.1472

Accepted Answer

A) 1.403460 
B) 0.712525 
C) 0.966674 
D) 1.158586 
A) 1.403460 
B) 0.712525 
C) 0.966674 
D) 1.158586

Graph the function. - $f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { - x }$ $Graph the function. - f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { - x }$

Write the equation in logarithmic form. - $5 ^ { 2 } = 25$

Find the number N. Round N to six decimal places. -log N = -1.4263

Evaluate. - $7 \left( 10 ^ { \log 2.9 } \right)$

Find the value obtained when 10 is raised to the given exponent. Round to three significant digits. --0.8514

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function. -f(x)= 4x

Write the equation in logarithmic form. - $343 ^ { 1 / 3 } = 7$

For the given functions f and g , find the indicated value. - f(x)=2x+4,g(x)=4+1 (g\circf)(1)

Write the equation in logarithmic form. - $10 ^ { 0.6931 } = 2$

Determine whether the given functions are inverses of each other. - $f ( x ) = x ^ { 4 } - 19 , \quad g ( x ) = \sqrt [ 4 ] { x - 19 }$

By changing the logarithm to exponential form, evaluate the common logarithm without the use of a calculator. -log 0.0001

Determine whether the function is a one-to-one function. - $\{ ( - 5,2 ) , ( - 4,2 ) , ( - 3,6 ) , ( - 2 , - 6 ) \}$

Use properties of logarithms to expand the logarithmic expression as much as possible. - $\log _ { 17 } \frac { 16 \sqrt { \mathrm { r } } } { \mathrm { s } }$

Find the common logarithm of the number. Round answer to four decimal places. -log 3447

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. - $\log _ { 3 } x ^ { 2 } = \log _ { 3 } ( 2 x + 8 )$

Find the unknown value. - $\log _ { 9 } \frac { 1 } { 81 } = y$

Determine whether the function is a one-to-one function. - $y = - x ^ { 2 } + 3$

Find the antilog of the logarithm. Round the answer to six decimal places. --0.1472

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Characteristics of Functions and Their Graphs

Conic Sections

Sequences, Series, and Probability

Filters

Exam 9: Exponential and Logarithmic Functions

Graph the function. - f(x)=(14)−xf ( x ) = \left( \frac { 1 } { 4 } \right) ^ { - x }f(x)=(41​)−x

Write the equation in logarithmic form. - 52=255 ^ { 2 } = 2552=25

Find the number N. Round N to six decimal places. -log N = -1.4263

Evaluate. - 7(10log⁡2.9)7 \left( 10 ^ { \log 2.9 } \right)7(10log2.9)

Find the value obtained when 10 is raised to the given exponent. Round to three significant digits. --0.8514

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function. -f(x)= 4x

Write the equation in logarithmic form. - 3431/3=7343 ^ { 1 / 3 } = 73431/3=7

For the given functions f and g , find the indicated value. - f(x)=2x+4,g(x)=4+1 (g\circf)(1)

Write the equation in logarithmic form. - 100.6931=210 ^ { 0.6931 } = 2100.6931=2

Determine whether the given functions are inverses of each other. - f(x)=x4−19,g(x)=x−194f ( x ) = x ^ { 4 } - 19 , \quad g ( x ) = \sqrt [ 4 ] { x - 19 }f(x)=x4−19,g(x)=4x−19​

By changing the logarithm to exponential form, evaluate the common logarithm without the use of a calculator. -log 0.0001

Determine whether the function is a one-to-one function. - {(−5,2),(−4,2),(−3,6),(−2,−6)}\{ ( - 5,2 ) , ( - 4,2 ) , ( - 3,6 ) , ( - 2 , - 6 ) \}{(−5,2),(−4,2),(−3,6),(−2,−6)}

Use properties of logarithms to expand the logarithmic expression as much as possible. - log⁡1716rs\log _ { 17 } \frac { 16 \sqrt { \mathrm { r } } } { \mathrm { s } }log17​s16r​​

Find the common logarithm of the number. Round answer to four decimal places. -log 3447

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. - log⁡3x2=log⁡3(2x+8)\log _ { 3 } x ^ { 2 } = \log _ { 3 } ( 2 x + 8 )log3​x2=log3​(2x+8)

Find the unknown value. - log⁡9181=y\log _ { 9 } \frac { 1 } { 81 } = ylog9​811​=y

Determine whether the function is a one-to-one function. - y=−x2+3y = - x ^ { 2 } + 3y=−x2+3

Find the antilog of the logarithm. Round the answer to six decimal places. --0.1472

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Characteristics of Functions and Their Graphs

Conic Sections

Sequences, Series, and Probability

Filters

Graph the function. - $f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { - x }$ $Graph the function. - f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { - x }$

Write the equation in logarithmic form. - $5 ^ { 2 } = 25$

Evaluate. - $7 \left( 10 ^ { \log 2.9 } \right)$

Write the equation in logarithmic form. - $343 ^ { 1 / 3 } = 7$

Write the equation in logarithmic form. - $10 ^ { 0.6931 } = 2$

Determine whether the given functions are inverses of each other. - $f ( x ) = x ^ { 4 } - 19 , \quad g ( x ) = \sqrt [ 4 ] { x - 19 }$

Determine whether the function is a one-to-one function. - $\{ ( - 5,2 ) , ( - 4,2 ) , ( - 3,6 ) , ( - 2 , - 6 ) \}$

Use properties of logarithms to expand the logarithmic expression as much as possible. - $\log _ { 17 } \frac { 16 \sqrt { \mathrm { r } } } { \mathrm { s } }$

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. - $\log _ { 3 } x ^ { 2 } = \log _ { 3 } ( 2 x + 8 )$

Find the unknown value. - $\log _ { 9 } \frac { 1 } { 81 } = y$

Determine whether the function is a one-to-one function. - $y = - x ^ { 2 } + 3$