Question 1

Find the antilog of the logarithm. Round the answer to six decimal places.
-1.0454

Accepted Answer

A) 0.090074 
B) 0.351551 
C) 1.272155 
D) 11.101969 
A) 0.090074 
B) 0.351551 
C) 1.272155 
D) 11.101969

Question 2

Use properties of logarithms to expand the logarithmic expression as much as possible.
-$\log _ { 6 } ( r + 7 ) ^ { 4 }$

Accepted Answer

A)  $4 \log _ { 6 } ( r + 7 )$ 
B)  $4 \left( \log _ { 6 } r + \log _ { 6 } 7 \right)$ 
C)  $\log _ { 6 } r ^ { 4 } + \log _ { 6 } 2401$ 2401 
D)  $\log _ { 6 } ( 4 r + 28 )$ 
A)  $4 \log _ { 6 } ( r + 7 )$ 
B)  $4 \left( \log _ { 6 } r + \log _ { 6 } 7 \right)$ 
C)  $\log _ { 6 } r ^ { 4 } + \log _ { 6 } 2401$ 2401 
D)  $\log _ { 6 } ( 4 r + 28 )$

Question 3

Solve the problem.
-The function $\mathrm { A } = \mathrm { A } _ { \mathrm { o } } \mathrm { e } ^ { - 0.0099 \mathrm { t } }$ models the amount in pounds of a particular radioactive material stored in a concrete vault, where t is the number of years since the material was put into the vault. If 900 pounds of the
Material are placed in the vault, how much time will need to pass for only 204 pounds to remain? Round to the
Nearest year.

Accepted Answer

A) 155 yr 
B) 300 yr 
C) 150 yr 
D) 160 yr 
A) 155 yr 
B) 300 yr 
C) 150 yr 
D) 160 yr

Question 4

Graph the function.
-$f ( x ) = 3 ^ { x + 1 }$

Accepted Answer

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

Question 5

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth.
-$$\log ( x + 5 ) = \log ( 5 x - 4 )$$

Accepted Answer

A)  $\frac { 3 } { 2 }$ 
B)  $\frac { 1 } { 4 }$ 
C)  $\frac { 9 } { 4 }$ 
D)  $- \frac { 9 } { 4 }$ 
A)  $\frac { 3 } { 2 }$ 
B)  $\frac { 1 } { 4 }$ 
C)  $\frac { 9 } { 4 }$ 
D)  $- \frac { 9 } { 4 }$

Question 6

Solve the problem.
-Find out how long it takes a $3000 investment to earn $300 interest if it is invested at 8% compounded quarterly. Round to the nearest tenth of a year. Use the formulala $\mathrm { A } = \mathrm { P } \left( 1 + \frac { \mathrm { r } } { \mathrm { n } } \right) ^ { \mathrm { nt } }$

Accepted Answer

A) 1.4 yr 
B) 1.6 yr 
C) 1.2 yr 
D) 1 yr 
A) 1.4 yr 
B) 1.6 yr 
C) 1.2 yr 
D) 1 yr

Question 7

Use properties of logarithms to expand the logarithmic expression as much as possible.
-$\log _ { 8 } \sqrt { \frac { x y } { 15 } }$

Accepted Answer

A)  $\frac { 1 } { 2 } \log _ { 8 } x y - \frac { 1 } { 2 } \log _ { 8 } 15$ 
B)  $\frac { 1 } { 2 } \log _ { 8 } x + \frac { 1 } { 2 } \log _ { 8 } y - \frac { 1 } { 2 } \log _ { 8 } 15$ 
C)  $\frac { 1 } { 2 } \log _ { 8 } x * \frac { 1 } { 2 } \log _ { 8 } y \div \frac { 1 } { 2 } \log _ { 8 } 15$ 
D)  $\frac { 1 } { 2 } \log _ { 8 } x + \frac { 1 } { 2 } \log _ { 8 } y - \log _ { 8 } 15$ 
A)  $\frac { 1 } { 2 } \log _ { 8 } x y - \frac { 1 } { 2 } \log _ { 8 } 15$ 
B)  $\frac { 1 } { 2 } \log _ { 8 } x + \frac { 1 } { 2 } \log _ { 8 } y - \frac { 1 } { 2 } \log _ { 8 } 15$ 
C)  $\frac { 1 } { 2 } \log _ { 8 } x * \frac { 1 } { 2 } \log _ { 8 } y \div \frac { 1 } { 2 } \log _ { 8 } 15$ 
D)  $\frac { 1 } { 2 } \log _ { 8 } x + \frac { 1 } { 2 } \log _ { 8 } y - \log _ { 8 } 15$

Question 8

Determine whether the function is a one-to-one function.
-$$y = ( x + 5 ) ^ { 2 }$$

Accepted Answer

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

Question 9

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function.
-$$f ( x ) = \frac { 2 } { x }$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { x } { 2 }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 2 } { \mathrm { x } }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - 2 \mathrm { x }$ 
D) not a one-to-one function 
A)  $f ^ { - 1 } ( x ) = \frac { x } { 2 }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 2 } { \mathrm { x } }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - 2 \mathrm { x }$ 
D) not a one-to-one function

Question 10

Write the equation in exponential form.
-$\log _ { 125 } 5 = \frac { 1 } { 3 }$

Accepted Answer

A)  $125 ^ { 1 / 3 } = 5$ 
B)  $5 ^ { 1 / 3 } = 125$ 
C)  $5 ^ { 125 } = \frac { 1 } { 3 }$ 
D)  $\left( \frac { 1 } { 3 } \right) ^ { 5 } = 125$ 
A)  $125 ^ { 1 / 3 } = 5$ 
B)  $5 ^ { 1 / 3 } = 125$ 
C)  $5 ^ { 125 } = \frac { 1 } { 3 }$ 
D)  $\left( \frac { 1 } { 3 } \right) ^ { 5 } = 125$

Question 11

Find the common logarithm of the number. Round answer to four decimal places.
-log 0.0649

Accepted Answer

A) -1.1945 
B) -2.7349 
C) -1.1811 
D) -1.1878 
A) -1.1945 
B) -2.7349 
C) -1.1811 
D) -1.1878

Question 12

Find the value obtained when 10 is raised to the given exponent. Round to three significant digits.
-2.5173

Accepted Answer

A) 327 
B) 328 
C) 329 
D) 330 
A) 327 
B) 328 
C) 329 
D) 330

Question 13

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function.
-$f ( x ) = x ^ { 3 } + 6$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } - 6$ 
B)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x + 6 }$ 
C)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x - 6 }$ 
D) not a one-to-one function 
A)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } - 6$ 
B)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x + 6 }$ 
C)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x - 6 }$ 
D) not a one-to-one function

Question 14

Find the unknown value.
-$\log _ { 1 / 2 } x = 3$

Accepted Answer

A)  $\frac { 1 } { 8 }$ 
B) 6 
C) 9 
D)  $\frac { 1 } { 6 }$ 
A)  $\frac { 1 } { 8 }$ 
B) 6 
C) 9 
D)  $\frac { 1 } { 6 }$

Question 15

Use properties of logarithms to expand the logarithmic expression as much as possible.
-$$\log _ { 2 } 13 ^ { - 5 }$$

Accepted Answer

A)  $- 10 \log 13$ 
B)  $13 \log _ { 2 } 5$ 
C)  $2 \log _ { 5 } 13$ 
D)  $- 5 \log _ { 2 } 13$ 
A)  $- 10 \log 13$ 
B)  $13 \log _ { 2 } 5$ 
C)  $2 \log _ { 5 } 13$ 
D)  $- 5 \log _ { 2 } 13$

Question 16

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function.
-f(x)= 3x + 4

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { x + 4 } { 3 }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } - 4 } { 3 }$ 
C)  $f ^ { - 1 } ( x ) = - \frac { x + 3 } { 4 }$ 
D) not a one-to-one function 
A)  $f ^ { - 1 } ( x ) = \frac { x + 4 } { 3 }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } - 4 } { 3 }$ 
C)  $f ^ { - 1 } ( x ) = - \frac { x + 3 } { 4 }$ 
D) not a one-to-one function

Question 17

Solve the problem.
-The amount of a radioactive substance present, in grams, at time t in months is given by the formula $y = 7000 ( 2 ) ^ { - 0.2 t }.$ Find the number Find the numberof grams present in 3 years. If necessary, round to three decimal places.

Accepted Answer

A) 4.761 
B) 461.828 
C) 4618.278 
D) 47.608 
A) 4.761 
B) 461.828 
C) 4618.278 
D) 47.608

Question 18

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 the pH = 4.4.

Accepted Answer

A)  $3.98 \times 10 ^ { - 5 }$ 
B)  $2.51 \times 10 ^ { - 4 }$ 
C)  $2.51 \times 10 ^ { - 5 }$ 
D)  $3.98 \times 10 ^ { - 4 }$ 
A)  $3.98 \times 10 ^ { - 5 }$ 
B)  $2.51 \times 10 ^ { - 4 }$ 
C)  $2.51 \times 10 ^ { - 5 }$ 
D)  $3.98 \times 10 ^ { - 4 }$

Question 19

Determine whether the function is a one-to-one function.
-$$y = - \frac { 3 } { 7 } x - 9$$

Accepted Answer

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

Question 20

Determine whether the function is a one-to-one function.
-$$y = x ^ { 2 } + 10 x + 29 , x \geq - 5$$

Accepted Answer

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

Find the antilog of the logarithm. Round the answer to six decimal places. -1.0454

Use properties of logarithms to expand the logarithmic expression as much as possible. - $\log _ { 6 } ( r + 7 ) ^ { 4 }$

Graph the function. - $f ( x ) = 3 ^ { x + 1 }$ $Graph the function. - f ( x ) = 3 ^ { x + 1 }$

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. - $\log ( x + 5 ) = \log ( 5 x - 4 )$

Use properties of logarithms to expand the logarithmic expression as much as possible. - $\log _ { 8 } \sqrt { \frac { x y } { 15 } }$

Determine whether the function is a one-to-one function. - $y = ( x + 5 ) ^ { 2 }$

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function. - $f ( x ) = \frac { 2 } { x }$

Write the equation in exponential form. - $\log _ { 125 } 5 = \frac { 1 } { 3 }$

Find the common logarithm of the number. Round answer to four decimal places. -log 0.0649

Find the value obtained when 10 is raised to the given exponent. Round to three significant digits. -2.5173

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function. - $f ( x ) = x ^ { 3 } + 6$

Find the unknown value. - $\log _ { 1 / 2 } x = 3$

Use properties of logarithms to expand the logarithmic expression as much as possible. - $\log _ { 2 } 13 ^ { - 5 }$

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function. -f(x)= 3x + 4

Solve the problem. -The amount of a radioactive substance present, in grams, at time t in months is given by the formula $y = 7000 ( 2 ) ^ { - 0.2 t }.$ Find the number Find the numberof grams present in 3 years. If necessary, round to three decimal places.

Determine whether the function is a one-to-one function. - $y = - \frac { 3 } { 7 } x - 9$

Determine whether the function is a one-to-one function. - $y = x ^ { 2 } + 10 x + 29 , x \geq - 5$

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

Find the antilog of the logarithm. Round the answer to six decimal places. -1.0454

Use properties of logarithms to expand the logarithmic expression as much as possible. - log⁡6(r+7)4\log _ { 6 } ( r + 7 ) ^ { 4 }log6​(r+7)4

Graph the function. - f(x)=3x+1f ( x ) = 3 ^ { x + 1 }f(x)=3x+1

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. - log⁡(x+5)=log⁡(5x−4)\log ( x + 5 ) = \log ( 5 x - 4 )log(x+5)=log(5x−4)

Use properties of logarithms to expand the logarithmic expression as much as possible. - log⁡8xy15\log _ { 8 } \sqrt { \frac { x y } { 15 } }log8​15xy​​

Determine whether the function is a one-to-one function. - y=(x+5)2y = ( x + 5 ) ^ { 2 }y=(x+5)2

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function. - f(x)=2xf ( x ) = \frac { 2 } { x }f(x)=x2​

Write the equation in exponential form. - log⁡1255=13\log _ { 125 } 5 = \frac { 1 } { 3 }log125​5=31​

Find the common logarithm of the number. Round answer to four decimal places. -log 0.0649

Find the value obtained when 10 is raised to the given exponent. Round to three significant digits. -2.5173

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function. - f(x)=x3+6f ( x ) = x ^ { 3 } + 6f(x)=x3+6

Find the unknown value. - log⁡1/2x=3\log _ { 1 / 2 } x = 3log1/2​x=3

Use properties of logarithms to expand the logarithmic expression as much as possible. - log⁡213−5\log _ { 2 } 13 ^ { - 5 }log2​13−5

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function. -f(x)= 3x + 4

Solve the problem. -The amount of a radioactive substance present, in grams, at time t in months is given by the formula y=7000(2)−0.2t.y = 7000 ( 2 ) ^ { - 0.2 t }.y=7000(2)−0.2t. Find the number Find the numberof grams present in 3 years. If necessary, round to three decimal places.

Determine whether the function is a one-to-one function. - y=−37x−9y = - \frac { 3 } { 7 } x - 9y=−73​x−9

Determine whether the function is a one-to-one function. - y=x2+10x+29,x≥−5y = x ^ { 2 } + 10 x + 29 , x \geq - 5y=x2+10x+29,x≥−5

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

Use properties of logarithms to expand the logarithmic expression as much as possible. - $\log _ { 6 } ( r + 7 ) ^ { 4 }$

Graph the function. - $f ( x ) = 3 ^ { x + 1 }$ $Graph the function. - f ( x ) = 3 ^ { x + 1 }$

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. - $\log ( x + 5 ) = \log ( 5 x - 4 )$

Use properties of logarithms to expand the logarithmic expression as much as possible. - $\log _ { 8 } \sqrt { \frac { x y } { 15 } }$

Determine whether the function is a one-to-one function. - $y = ( x + 5 ) ^ { 2 }$

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function. - $f ( x ) = \frac { 2 } { x }$

Write the equation in exponential form. - $\log _ { 125 } 5 = \frac { 1 } { 3 }$

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function. - $f ( x ) = x ^ { 3 } + 6$

Find the unknown value. - $\log _ { 1 / 2 } x = 3$

Use properties of logarithms to expand the logarithmic expression as much as possible. - $\log _ { 2 } 13 ^ { - 5 }$

Solve the problem. -The amount of a radioactive substance present, in grams, at time t in months is given by the formula $y = 7000 ( 2 ) ^ { - 0.2 t }.$ Find the number Find the numberof grams present in 3 years. If necessary, round to three decimal places.

Determine whether the function is a one-to-one function. - $y = - \frac { 3 } { 7 } x - 9$

Determine whether the function is a one-to-one function. - $y = x ^ { 2 } + 10 x + 29 , x \geq - 5$