Question 1

Find the intervals on which the given function is increasing and the intervals on which it is decreasing. f ( x ) = $-$ 2 x 2 $-$ 16 x $-$ 49

Accepted Answer

A)  $\text { Increasing on } ( - \infty , - 4 ] \text { and decreasing on } [ - 4 , \infty )$ . 
B)  $\text { Increasing on } [ - 4 , \infty ) \text { and decreasing on } ( - \infty , - 4 ]$ . 
C)  $\text { No correct answer }$ . 
A)  $\text { Increasing on } ( - \infty , - 4 ] \text { and decreasing on } [ - 4 , \infty )$ . 
B)  $\text { Increasing on } [ - 4 , \infty ) \text { and decreasing on } ( - \infty , - 4 ]$ . 
C)  $\text { No correct answer }$ .

Question 2

Two functions that are inverses of each other are mirror images with reference to the y axis.

Accepted Answer

A) True 
 B)False

Question 3

Solve the equation. log 10 ( 2 x $-$ 27 ) $-$ log 10 ( x $-$ 4 ) = 1

Accepted Answer

A)  $x = \frac { 17 } { 8 }$ 
B)  $x = \frac { 13 } { 8 }$ 
C)  $x = \frac { 11 } { 8 }$ 
A)  $x = \frac { 17 } { 8 }$ 
B)  $x = \frac { 13 } { 8 }$ 
C)  $x = \frac { 11 } { 8 }$

Question 4

Use a calculator to find each common logarithm. Express answer to four decimal places. $\log 0.00058$

Accepted Answer

The answer of Use a calculator to find each common...

Question 5

Solve the equation. $256 ^ { x } = 1,024$

Accepted Answer

The answer of Solve the equation. \(256 ^ { x...

Question 6

Solve the logarithmic equation. $\log ( \sqrt [ 3 ] { x } ) = \sqrt { \log ( x ) }$

Accepted Answer

A)  x = 1 
B)  x = 1,000,000,000, x = 1 
C)  x = 10,000,000, x = $-$ 1 
D)  x = 100,000,000 
A)  x = 1 
B)  x = 1,000,000,000, x = 1 
C)  x = 10,000,000, x = $-$ 1 
D)  x = 100,000,000

Question 7

Solve the logarithmic equation. $\log ( x + 3 ) - \log ( 2 x + 2 ) = \log x$

Accepted Answer

A)  $x = 2$ 
B)  $x = 1$ 
C)  $x = 0$ 
D)  $x = 4$ 
A)  $x = 2$ 
B)  $x = 1$ 
C)  $x = 0$ 
D)  $x = 4$

Question 8

Use a calculator to find each common logarithm. Express answer to four decimal places. $\ln 0.000263$

Accepted Answer

A)  -8.2434 
B)  -8.3066 
C)  -8.2203 
D)  -8.2485 
E)  -8.2761 
A)  -8.2434 
B)  -8.3066 
C)  -8.2203 
D)  -8.2485 
E)  -8.2761

Question 9

Evaluate the expression. $6 ^ { \log _ { 6 } 2 }$

Accepted Answer

The answer of Evaluate the expression. \(6 ^ { \log...

Question 10

Solve the exponential equation and express approximate solutions to the nearest hundredth. 9 x + 6 = 38

Accepted Answer

A)  x = 0.63 
B)  x = 0.48 
C)  x = 0.84 
D)  x = 0.51 
E)  x = 0.58 
A)  x = 0.63 
B)  x = 0.48 
C)  x = 0.84 
D)  x = 0.51 
E)  x = 0.58

Question 11

Write the logarithmic statement in exponential form. log 10 0.001 = $-$ 3

Accepted Answer

The answer of Write the logarithmic statement in exponential form....

Question 12

Interest compounded annually is found using the formula $A = P ( 1 + r t )$

Accepted Answer

A) True 
 B)False

Question 13

Solve the logarithmic equation and express irrational solutions in lowest radical form. log ( x + 7 ) = log ( 4 ) $-$ log ( 2 x $-$ 14 )

Accepted Answer

The answer of Solve the logarithmic equation and express irrational...

Question 14

Solve the logarithmic equation. ln( 4 x + 4 ) = ln 5 + ln ( x $-$ 2 )

Accepted Answer

The answer of Solve the logarithmic equation. ln( 4 x...

Question 15

Use your calculator to find x when given ln x . Please give the answer to four decimal places. $\ln x = 2.7512$

Accepted Answer

A)  15.6914 
B)  15.6514 
C)  15.6614 
D)  15.6814 
E)  15.7114 
A)  15.6914 
B)  15.6514 
C)  15.6614 
D)  15.6814 
E)  15.7114

Question 16

The equation $P ( a ) = 14.7 e ^ { - 0.21 a }$ , where a is the altitude above sea level measured in miles, yields the atmospheric pressure in pounds per square inch. If the atmospheric pressure at Cheyenne, Wyoming, is approximately 11.57 pounds per square inch, find that city s altitude above sea level. Express your answer to the nearest hundred feet.

Accepted Answer

A)  6,400 feet 
B)  6,000 feet 
C)  6,200 feet 
D)  5,700 feet 
E)  5,900 feet 
A)  6,400 feet 
B)  6,000 feet 
C)  6,200 feet 
D)  5,700 feet 
E)  5,900 feet

Question 17

Write the logarithmic statement in exponential form. log 101,000 = 3

Accepted Answer

Question 18

Solve the equation. $\left( 3 ^ { 4 x - 4 } \right) \left( 3 ^ { x + 1 } \right) = 27$

Accepted Answer

A)  $x = - \frac { 6 } { 5 }$ 
B)  $x = \frac { 11 } { 5 }$ 
C)  $x = - \frac { 1 } { 5 }$ 
D)  $x = \frac { 6 } { 5 }$ 
A)  $x = - \frac { 6 } { 5 }$ 
B)  $x = \frac { 11 } { 5 }$ 
C)  $x = - \frac { 1 } { 5 }$ 
D)  $x = \frac { 6 } { 5 }$

Question 19

Approximate the following logarithm to three decimal places. $\log _ { 6 } 0.16$

Accepted Answer

A)  -1.023 
B)  -0.993 
C)  -1.033 
D)  -1.043 
E)  -0.973 
A)  -1.023 
B)  -0.993 
C)  -1.033 
D)  -1.043 
E)  -0.973

Question 20

Find f - -1 ( x ). f ( x ) = $-$ 9 x $-$ 4

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { x + 4 } { 9 }$ 
B)  $f ^ { - 1 } ( x ) = - \frac { x + 4 } { 9 }$ 
C)  $f ^ { - 1 } ( x ) = - \frac { x } { 9 } + \frac { 4 } { 9 }$ 
A)  $f ^ { - 1 } ( x ) = \frac { x + 4 } { 9 }$ 
B)  $f ^ { - 1 } ( x ) = - \frac { x + 4 } { 9 }$ 
C)  $f ^ { - 1 } ( x ) = - \frac { x } { 9 } + \frac { 4 } { 9 }$

Find the intervals on which the given function is increasing and the intervals on which it is decreasing. f ( x ) = $-$ 2 x 2 $-$ 16 x $-$ 49

Two functions that are inverses of each other are mirror images with reference to the y axis.

Solve the equation. log 10 ( 2 x $-$ 27 ) $-$ log 10 ( x $-$ 4 ) = 1

Use a calculator to find each common logarithm. Express answer to four decimal places. $\log 0.00058$

Solve the equation. $256 ^ { x } = 1,024$

Solve the logarithmic equation. $\log ( \sqrt [ 3 ] { x } ) = \sqrt { \log ( x ) }$

Solve the logarithmic equation. $\log ( x + 3 ) - \log ( 2 x + 2 ) = \log x$

Use a calculator to find each common logarithm. Express answer to four decimal places. $\ln 0.000263$

Evaluate the expression. $6 ^ { \log _ { 6 } 2 }$

Solve the exponential equation and express approximate solutions to the nearest hundredth. 9 ^x + 6 = 38

Write the logarithmic statement in exponential form. log 10 0.001 = $-$ 3

Interest compounded annually is found using the formula $A = P ( 1 + r t )$

Solve the logarithmic equation and express irrational solutions in lowest radical form. log ( x + 7 ) = log ( 4 ) $-$ log ( 2 x $-$ 14 )

Solve the logarithmic equation. ln( 4 x + 4 ) = ln 5 + ln ( x $-$ 2 )

Use your calculator to find x when given ln x . Please give the answer to four decimal places. $\ln x = 2.7512$

Write the logarithmic statement in exponential form. log ₁₀1,000 = 3

Solve the equation. $\left( 3 ^ { 4 x - 4 } \right) \left( 3 ^ { x + 1 } \right) = 27$

Approximate the following logarithm to three decimal places. $\log _ { 6 } 0.16$

Find f - -1 ( x ). f ( x ) = $-$ 9 x $-$ 4

Some Basic Concepts of Arithmetic and Algebra

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Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

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Exponents and Radicals

Quadratic Equations and Inequalities

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Exam 14: Exponential and Logarithmic Functions

Find the intervals on which the given function is increasing and the intervals on which it is decreasing. f ( x ) = −-− 2 x 2 −-− 16 x −-− 49

Two functions that are inverses of each other are mirror images with reference to the y axis.

Solve the equation. log 10 ( 2 x −-− 27 ) −-− log 10 ( x −-− 4 ) = 1

Use a calculator to find each common logarithm. Express answer to four decimal places. log⁡0.00058\log 0.00058log0.00058

Solve the equation. 256x=1,024256 ^ { x } = 1,024256x=1,024

Solve the logarithmic equation. log⁡(x3)=log⁡(x)\log ( \sqrt [ 3 ] { x } ) = \sqrt { \log ( x ) }log(3x​)=log(x)​

Solve the logarithmic equation. log⁡(x+3)−log⁡(2x+2)=log⁡x\log ( x + 3 ) - \log ( 2 x + 2 ) = \log xlog(x+3)−log(2x+2)=logx

Use a calculator to find each common logarithm. Express answer to four decimal places. ln⁡0.000263\ln 0.000263ln0.000263

Evaluate the expression. 6log⁡626 ^ { \log _ { 6 } 2 }6log6​2

Solve the exponential equation and express approximate solutions to the nearest hundredth. 9 x + 6 = 38

Write the logarithmic statement in exponential form. log 10 0.001 = −-− 3

Interest compounded annually is found using the formula A=P(1+rt)A = P ( 1 + r t )A=P(1+rt)

Solve the logarithmic equation and express irrational solutions in lowest radical form. log ( x + 7 ) = log ( 4 ) −-− log ( 2 x −-− 14 )

Solve the logarithmic equation. ln( 4 x + 4 ) = ln 5 + ln ( x −-− 2 )

Use your calculator to find x when given ln x . Please give the answer to four decimal places. ln⁡x=2.7512\ln x = 2.7512lnx=2.7512

Write the logarithmic statement in exponential form. log 101,000 = 3

Solve the equation. (34x−4)(3x+1)=27\left( 3 ^ { 4 x - 4 } \right) \left( 3 ^ { x + 1 } \right) = 27(34x−4)(3x+1)=27

Approximate the following logarithm to three decimal places. log⁡60.16\log _ { 6 } 0.16log6​0.16

Find f - -1 ( x ). f ( x ) = −-− 9 x −-− 4

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Systems of Equations: Matrices and Determinants

Filters

Find the intervals on which the given function is increasing and the intervals on which it is decreasing. f ( x ) = $-$ 2 x 2 $-$ 16 x $-$ 49

Solve the equation. log 10 ( 2 x $-$ 27 ) $-$ log 10 ( x $-$ 4 ) = 1

Use a calculator to find each common logarithm. Express answer to four decimal places. $\log 0.00058$

Solve the equation. $256 ^ { x } = 1,024$

Solve the logarithmic equation. $\log ( \sqrt [ 3 ] { x } ) = \sqrt { \log ( x ) }$

Solve the logarithmic equation. $\log ( x + 3 ) - \log ( 2 x + 2 ) = \log x$

Use a calculator to find each common logarithm. Express answer to four decimal places. $\ln 0.000263$

Evaluate the expression. $6 ^ { \log _ { 6 } 2 }$

Solve the exponential equation and express approximate solutions to the nearest hundredth. 9 ^x + 6 = 38

Write the logarithmic statement in exponential form. log 10 0.001 = $-$ 3

Interest compounded annually is found using the formula $A = P ( 1 + r t )$

Solve the logarithmic equation and express irrational solutions in lowest radical form. log ( x + 7 ) = log ( 4 ) $-$ log ( 2 x $-$ 14 )

Solve the logarithmic equation. ln( 4 x + 4 ) = ln 5 + ln ( x $-$ 2 )

Use your calculator to find x when given ln x . Please give the answer to four decimal places. $\ln x = 2.7512$

Write the logarithmic statement in exponential form. log ₁₀1,000 = 3

Solve the equation. $\left( 3 ^ { 4 x - 4 } \right) \left( 3 ^ { x + 1 } \right) = 27$

Approximate the following logarithm to three decimal places. $\log _ { 6 } 0.16$

Find f - -1 ( x ). f ( x ) = $-$ 9 x $-$ 4