Question 1

All exponential equations can be written as logarithmic equations.

Accepted Answer

A) True 
 B)False

Question 2

Graph the exponential function. $f ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }$

Accepted Answer

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

Question 3

Find f -1 ( x ). $f ( x ) = x ^ { 2 } + 8 \text { for } x \geq 0$

Accepted Answer

The answer of Find f -1 ( x ). \(f...

Question 4

Determine whether the function f is one-to-one. f ( x ) = x 7 Please enter yes or no .

Accepted Answer

Question 5

Solve the logarithmic equation and express irrational solutions in lowest radical form. log ( x + 9 ) = log ( 6 ) $-$ log ( 3 x $-$ 27 )

Accepted Answer

A)  $x = \sqrt { 79 }$ 
B)  $x = 9$ 
C)  $x = 83$ 
D)  $x = \sqrt { 83 }$ 
A)  $x = \sqrt { 79 }$ 
B)  $x = 9$ 
C)  $x = 83$ 
D)  $x = \sqrt { 83 }$

Question 6

Mark became overextended in his gambling debt and could not pay $400 he owed. The loan person said he could have three weeks to pay off the $400 at 6% interest per week compounded continuously. How much will Mark have to pay at the end of the three weeks? Please round the answer to the nearest hundredth. $__________

Accepted Answer

The answer of Mark became overextended in his gambling debt...

Question 7

Verify that the two given functions are inverses of each other. $f ( x ) = \frac { 2 } { 2 x - 1 } \text { for } x > \frac { 1 } { 2 } \text { and }$ $g ( x ) = \frac { x + 2 } { 2 x } \text { for } x > 0$

Accepted Answer

The answer of Verify that the two given functions are...

Question 8

For a certain culture the equation $Q ( t ) = Q _ { 0 } e ^ { 0.9 t }$ , where Q 0 is an initial number of bacteria and t is time measured in hours, yields the number of bacteria as a function of time. How long will it take 600 bacteria to increase to 3,600? Please round the answer to the nearest tenth.

Accepted Answer

A)  2.0 hours 
B)  1.0 hours 
C)  7.0 hours 
D)  5.0 hours 
E)  4.0 hours 
A)  2.0 hours 
B)  1.0 hours 
C)  7.0 hours 
D)  5.0 hours 
E)  4.0 hours

Question 9

Solve the exponential equation and express solution to the nearest hundredth. $7 ^ { x } = 166$

Accepted Answer

A)  x = 3.03 
B)  x = 2.63 
C)  x = 2.83 
D)  x = 3.23 
E)  x = 2.13 
A)  x = 3.03 
B)  x = 2.63 
C)  x = 2.83 
D)  x = 3.23 
E)  x = 2.13

Question 10

A problem compounded quarterly is found by the formula $A = p \left( 1 + \frac { r } { 4 } \right) ^ { 4 t }$ .

Accepted Answer

A) True 
 B)False

Question 11

Solve the equation. $5 ^ { 2 x } = 625$

Accepted Answer

The answer of Solve the equation. \(5 ^ { 2...

Question 12

Solve the equation. $81 ^ { x } = 243$

Accepted Answer

A)  $x = - \frac { 5 } { 4 }$ 
B)  $x = \frac { 9 } { 4 }$ 
C)  $x = \frac { 5 } { 4 }$ 
D)  $x = \frac { 1 } { 4 }$ 
A)  $x = - \frac { 5 } { 4 }$ 
B)  $x = \frac { 9 } { 4 }$ 
C)  $x = \frac { 5 } { 4 }$ 
D)  $x = \frac { 1 } { 4 }$

Question 13

The natural logarithmic function is the inverse of the natural exponential function.

Accepted Answer

A) True 
 B)False

Question 14

Determine whether the function f is one-to-one. f ( x ) = 7 x + 3 Please enter yes or no .

Accepted Answer

The answer of Determine whether the function f is one-to-one....

Question 15

Solve the exponential equation and express approximate solutions to the nearest hundredth. e x - 5 = 38

Accepted Answer

Question 16

A function that has exactly one value of x associated with each value of $f ( x )$ is a one-to-one function.

Accepted Answer

A) True 
 B)False

Question 17

Use a calculator to find each common logarithm. Express answer to four decimal places. $\log x = - 2.1956$

Accepted Answer

A)  0.0064 
B)  -0.0568 
C)  0.0013 
D)  0.0295 
E)  -0.0263 
A)  0.0064 
B)  -0.0568 
C)  0.0013 
D)  0.0295 
E)  -0.0263

Question 18

Find f - -1 ( x ). $f ( x ) = - \frac { 7 } { 8 } x$

Accepted Answer

The answer of Find f - -1 ( x )....

Question 19

The equation $m ^ { q } = n$ is equivalent to the $\log _ { n } m = q$ .

Accepted Answer

A) True 
 B)False

Question 20

Solve the equation. log 12 ( x + 1 ) + log 12 ( x $-$ 36 ) = 3

Accepted Answer

A)  x = 65 
B)  x = 62 
C)  x = 63 
D)  x = 66 
A)  x = 65 
B)  x = 62 
C)  x = 63 
D)  x = 66

All exponential equations can be written as logarithmic equations.

Graph the exponential function. $f ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }$

Find f -1 ( x ). $f ( x ) = x ^ { 2 } + 8 \text { for } x \geq 0$

Determine whether the function f is one-to-one. f ( x ) = x ⁷ Please enter yes or no .

Solve the logarithmic equation and express irrational solutions in lowest radical form. log ( x + 9 ) = log ( 6 ) $-$ log ( 3 x $-$ 27 )

Verify that the two given functions are inverses of each other. $f ( x ) = \frac { 2 } { 2 x - 1 } \text { for } x > \frac { 1 } { 2 } \text { and }$ $g ( x ) = \frac { x + 2 } { 2 x } \text { for } x > 0$

Solve the exponential equation and express solution to the nearest hundredth. $7 ^ { x } = 166$

A problem compounded quarterly is found by the formula $A = p \left( 1 + \frac { r } { 4 } \right) ^ { 4 t }$ .

Solve the equation. $5 ^ { 2 x } = 625$

Solve the equation. $81 ^ { x } = 243$

The natural logarithmic function is the inverse of the natural exponential function.

Determine whether the function f is one-to-one. f ( x ) = 7 x + 3 Please enter yes or no .

Solve the exponential equation and express approximate solutions to the nearest hundredth. e^{x - 5} = 38

A function that has exactly one value of x associated with each value of $f ( x )$ is a one-to-one function.

Use a calculator to find each common logarithm. Express answer to four decimal places. $\log x = - 2.1956$

Find f - -1 ( x ). $f ( x ) = - \frac { 7 } { 8 } x$

The equation $m ^ { q } = n$ is equivalent to the $\log _ { n } m = q$ .

Solve the equation. log 12 ( x + 1 ) + log 12 ( x $-$ 36 ) = 3

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

Exam 14: Exponential and Logarithmic Functions

All exponential equations can be written as logarithmic equations.

Graph the exponential function. f(x)=(13)xf ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }f(x)=(31​)x

Find f -1 ( x ). f(x)=x2+8 for x≥0f ( x ) = x ^ { 2 } + 8 \text { for } x \geq 0f(x)=x2+8 for x≥0

Determine whether the function f is one-to-one. f ( x ) = x 7 Please enter yes or no .

Solve the logarithmic equation and express irrational solutions in lowest radical form. log ( x + 9 ) = log ( 6 ) −-− log ( 3 x −-− 27 )

Verify that the two given functions are inverses of each other. f(x)=22x−1 for x>12 and f ( x ) = \frac { 2 } { 2 x - 1 } \text { for } x > \frac { 1 } { 2 } \text { and }f(x)=2x−12​ for x>21​ and g(x)=x+22x for x>0g ( x ) = \frac { x + 2 } { 2 x } \text { for } x > 0g(x)=2xx+2​ for x>0

Solve the exponential equation and express solution to the nearest hundredth. 7x=1667 ^ { x } = 1667x=166

A problem compounded quarterly is found by the formula A=p(1+r4)4tA = p \left( 1 + \frac { r } { 4 } \right) ^ { 4 t }A=p(1+4r​)4t .

Solve the equation. 52x=6255 ^ { 2 x } = 62552x=625

Solve the equation. 81x=24381 ^ { x } = 24381x=243

The natural logarithmic function is the inverse of the natural exponential function.

Determine whether the function f is one-to-one. f ( x ) = 7 x + 3 Please enter yes or no .

Solve the exponential equation and express approximate solutions to the nearest hundredth. e x - 5 = 38

A function that has exactly one value of x associated with each value of f(x)f ( x )f(x) is a one-to-one function.

Use a calculator to find each common logarithm. Express answer to four decimal places. log⁡x=−2.1956\log x = - 2.1956logx=−2.1956

Find f - -1 ( x ). f(x)=−78xf ( x ) = - \frac { 7 } { 8 } xf(x)=−87​x

The equation mq=nm ^ { q } = nmq=n is equivalent to the log⁡nm=q\log _ { n } m = qlogn​m=q .

Solve the equation. log 12 ( x + 1 ) + log 12 ( x −-− 36 ) = 3

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

Graph the exponential function. $f ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }$

Find f -1 ( x ). $f ( x ) = x ^ { 2 } + 8 \text { for } x \geq 0$

Determine whether the function f is one-to-one. f ( x ) = x ⁷ Please enter yes or no .

Solve the logarithmic equation and express irrational solutions in lowest radical form. log ( x + 9 ) = log ( 6 ) $-$ log ( 3 x $-$ 27 )

Verify that the two given functions are inverses of each other. $f ( x ) = \frac { 2 } { 2 x - 1 } \text { for } x > \frac { 1 } { 2 } \text { and }$ $g ( x ) = \frac { x + 2 } { 2 x } \text { for } x > 0$

Solve the exponential equation and express solution to the nearest hundredth. $7 ^ { x } = 166$

A problem compounded quarterly is found by the formula $A = p \left( 1 + \frac { r } { 4 } \right) ^ { 4 t }$ .

Solve the equation. $5 ^ { 2 x } = 625$

Solve the equation. $81 ^ { x } = 243$

Solve the exponential equation and express approximate solutions to the nearest hundredth. e^{x - 5} = 38

A function that has exactly one value of x associated with each value of $f ( x )$ is a one-to-one function.

Use a calculator to find each common logarithm. Express answer to four decimal places. $\log x = - 2.1956$

Find f - -1 ( x ). $f ( x ) = - \frac { 7 } { 8 } x$

The equation $m ^ { q } = n$ is equivalent to the $\log _ { n } m = q$ .

Solve the equation. log 12 ( x + 1 ) + log 12 ( x $-$ 36 ) = 3