Question 1

Evaluate   .

Accepted Answer

A)    
B)    
C)    
D)  3 
A)    
B)    
C)    
D)  3 D

Question 2

Let   . Solve   for x.

Accepted Answer

A)    
B)  {   } 
C)    
D)  {   } 
A)    
B)  {   } 
C)    
D)  {   } A

Question 3

Write log9(28) - log9(7) as a single logarithm.

Accepted Answer

A)  935 
B)  The logarithms cannot be combined. 
C)  log9(4) 
D)  log9(35) 
A)  935 
B)  The logarithms cannot be combined. 
C)  log9(4) 
D)  log9(35) C

Question 4

Write log(16) in terms of log(4).

Accepted Answer

A)  2log(4) 
B)  The expression cannot be written in terms of log(4). 
C)  log(4) + 2 
D)  log2(4) 
A)  2log(4) 
B)  The expression cannot be written in terms of log(4). 
C)  log(4) + 2 
D)  log2(4)

Question 5

Which of the following is the correct graph of   ?

Accepted Answer

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

Question 6

Write 25 = 32 as a logarithmic equation.

Accepted Answer

A)  log25 = 32 
B)  log232 = 2 
C)  log532 = 2 
D)  log232 = 5 
A)  log25 = 32 
B)  log232 = 2 
C)  log532 = 2 
D)  log232 = 5

Question 7

Simplify ln(e12).

Accepted Answer

A)  12 
B)  -12 
C)  e 
D)  12 ln(e12) 
A)  12 
B)  -12 
C)  e 
D)  12 ln(e12)

Question 8

Write log864 = 2 as an exponential equation.

Accepted Answer

A)  82 = 64 
B)  82 = 8 
C)  642 = 8 
D)  642 = 64 
A)  82 = 64 
B)  82 = 8 
C)  642 = 8 
D)  642 = 64

Question 9

Let   . Find g(-2).

Accepted Answer

A)  1 
B)  8 
C)  4 
D)  2 
A)  1 
B)  8 
C)  4 
D)  2

Question 10

Which of the following is the correct graph of   ?

Accepted Answer

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

Question 11

Solve -8-6-x = -64.

Accepted Answer

A)  {-8} 
B)  {0} 
C)  {-6} 
D)  {-7} 
A)  {-8} 
B)  {0} 
C)  {-6} 
D)  {-7}

Question 12

Rewrite   as a single logarithm.

Accepted Answer

A) 
  
B) 
  
C)  The expression cannot be written as a single logarithm. 
D) 
  
A) 
  
B) 
  
C)  The expression cannot be written as a single logarithm. 
D)

Question 13

If $7,000 is deposited in an account paying 5% compounded quarterly, then what amount will be in the account after 5 years?

Accepted Answer

A)  $9,122.26 
B)  $6,998.26 
C)  $8,974.26 
D)  $18,573.08 
A)  $9,122.26 
B)  $6,998.26 
C)  $8,974.26 
D)  $18,573.08

Question 14

The level of sound in decibels (db) is given by the formula   , where I is the sound intensity in watts per square meter. If the sound intensity of a jet airplane is 0.001 watts per square meter at a distance of 170 meters, what is the level of the sound at this point in db, rounded to the nearest tenth?

Accepted Answer

A)  74.7 
B)  77.2 
C)  90.0 
D)  81.1 
A)  74.7 
B)  77.2 
C)  90.0 
D)  81.1

Question 15

Let   . Find k(-3) rounded to 4 decimal places.

Accepted Answer

A)  0.0498 
B)  0.1353 
C)  7.3891 
D)  0.7408 
A)  0.0498 
B)  0.1353 
C)  7.3891 
D)  0.7408

Question 16

Solve log7(x - 24) + log7(x + 24) = 2.

Accepted Answer

A)  {26} 
B)  {-25} 
C)  {25} 
D)  {27} 
A)  {26} 
B)  {-25} 
C)  {25} 
D)  {27}

Question 17

Solve ex + 4 = 7.

Accepted Answer

A)  {ln(7) - 4} 
B)  {ln(3)} 
C)  {4 ln(7)} 
D)  {ln(7) + 4} 
A)  {ln(7) - 4} 
B)  {ln(3)} 
C)  {4 ln(7)} 
D)  {ln(7) + 4}

Question 18

The number of grams of a radioactive substance in charcoal from an ancient campfire after t years is given by   . If the sample has only 15 grams of radioactive substance, then when was the campfire used?

Accepted Answer

A)  5,752 years ago 
B)  4,706 years ago 
C)  12,040 years ago 
D)  5,229 years ago 
A)  5,752 years ago 
B)  4,706 years ago 
C)  12,040 years ago 
D)  5,229 years ago

Question 19

Solve:

Accepted Answer

A)    
B)  {2} 
C)    
D)    
A)    
B)  {2} 
C)    
D)

Question 20

Solve log3(x2 - 1) = 2 + log3(x2 + 2).

Accepted Answer

A)  {-2, 1} 
B)  Ø 
C)  {19} 
D)  {4, 7} 
A)  {-2, 1} 
B)  Ø 
C)  {19} 
D)  {4, 7}

Exam 12: Section 1: Exponential and Logarithmic Functions

Evaluate .

Let . Solve for x.

Write log9(28) - log9(7) as a single logarithm.

Write log(16) in terms of log(4).

Which of the following is the correct graph of ?

Write 25 = 32 as a logarithmic equation.

Simplify ln(e12).

Write log864 = 2 as an exponential equation.

Let . Find g(-2).

Which of the following is the correct graph of ?

Solve -8-6-x = -64.

Rewrite as a single logarithm.

If $7,000 is deposited in an account paying 5% compounded quarterly, then what amount will be in the account after 5 years?

Let . Find k(-3) rounded to 4 decimal places.

Solve log7(x - 24) + log7(x + 24) = 2.

Solve ex + 4 = 7.

The number of grams of a radioactive substance in charcoal from an ancient campfire after t years is given by . If the sample has only 15 grams of radioactive substance, then when was the campfire used?

Solve:

Solve log3(x2 - 1) = 2 + log3(x2 + 2).

Section 1: Real Numbers and Their Properties

Section 2: Real Numbers and Their Properties

Section 1: Linear Equations and Inequalities in One Variable

Section 2: Linear Equations and Inequalities in One Variable

Section 1: Linear Equations and Inequalities in Two Variables

Section 2: Linear Equations and Inequalities in Two Variables

Section 1: Exponents and Polynomials

Section 2: Exponents and Polynomials

Section 1: Factoring

Section 2: Factoring

Section 1: Rational Expressions

Section 2: Rational Expressions

Section 1: Systems of Linear Equations

Section 2: Systems of Linear Equations

Section 1: More on Inequalities

Section 2: More on Inequalities

Section 1: Radicals and Rational Exponents

Section 2: Radicals and Rational Exponents

Section 1: Quadratic Equations and Inequalities

Section 2: Quadratic Equations and Inequalities

Section 1: Functions

Section 2: Functions

Section 2: Exponential and Logarithmic Functions

Section 1: Nonlinear Systems and the Conic Sections

Section 2: Nonlinear Systems and the Conic Sections

Section 1: Sequences and Series Available Online at Www.mhhe.com/dugopolski

Section 2: Sequences and Series Available Online at Www.mhhe.com/dugopolski

Mathematical Problem Set

Algebraic Equations and Problem Solving

Algebra and Math Problems

Algebraic Equation Practice

Filters

Write log₉(28) - log₉(7) as a single logarithm.

Write 2⁵ = 32 as a logarithmic equation.

Simplify ln(e¹²).

Write log₈64 = 2 as an exponential equation.

Solve -8^-6-^x = -64.

Solve log₇(x - 24) + log₇(x + 24) = 2.

Solve e^x^{+ 4} = 7.

Solve log₃(x² - 1) = 2 + log₃(x² + 2).