Question 1

Graph the function   . Remember that the graph of   is given.

Accepted Answer

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

Question 2

Solve the logarithmic equation. Check the solution.

Accepted Answer

A)    10 
B)    1,000 
C)    10,000 
D)    100 
E)    1 
A)    10 
B)    1,000 
C)    10,000 
D)    100 
E)    1

Question 3

Assume that   and   . Use the change-of-base formula to find the logarithm to four decimal places.

Accepted Answer

A)  1.6812 
B)  0.5579 
C)  2.4771 
D)  1.7925 
A)  1.6812 
B)  0.5579 
C)  2.4771 
D)  1.7925

Question 4

Business equipment is often depreciated using the double declining-balance method. In this method, a piece of equipment with a life expectancy of N years, costing C dollars, will depreciate to a value of V dollars in n years, where n is given by the formula:   A computer that cost $14,000 has a life expectancy of 5 years. If it has depreciated to a value of $1,600, how old is it? Round the answer to the nearest tenth of the year.

Accepted Answer

A)  4.2 years old 
B)  6.1 years old 
C)  2.5 years old 
D)  5.3 years old 
E)  4.7 years old 
A)  4.2 years old 
B)  6.1 years old 
C)  2.5 years old 
D)  5.3 years old 
E)  4.7 years old

Question 5

Find the value, if possible. Give the answer to four decimal places.

Accepted Answer

A)  3.2484 
B)  3.3051 
C)  3.2088 
D)  3.2677 
E)  none of these 
A)  3.2484 
B)  3.3051 
C)  3.2088 
D)  3.2677 
E)  none of these

Question 6

A piece of machinery valued at $38,000 depreciates at a rate of 7% yearly. How long will it take until it has a value of $19,000? Please round the answer to the nearest tenth.

Accepted Answer

A)  11.9 years 
B)  14.9 years 
C)  12.9 years 
D)  9.9 years 
E)  8.9 years 
A)  11.9 years 
B)  14.9 years 
C)  12.9 years 
D)  9.9 years 
E)  8.9 years

Question 7

Solve the exponential equation and express solution to the nearest hundredth.

Accepted Answer

A)  x = 1.76 
B)  x = 2.16 
C)  x = 1.26 
D)  x = 2.36 
E)  x = 1.96 
A)  x = 1.76 
B)  x = 2.16 
C)  x = 1.26 
D)  x = 2.36 
E)  x = 1.96

Question 8

How long will it take $800 to double itself if it is invested at 5% interest compounded semiannually? Please round the answer to the nearest tenth.

Accepted Answer

A)  14.0 years 
B)  17.0 years 
C)  14.5 years 
D)  13.0 years 
E)  15.0 years 
A)  14.0 years 
B)  17.0 years 
C)  14.5 years 
D)  13.0 years 
E)  15.0 years

Question 9

Use a calculator to find each common logarithm. Express answer to four decimal places.

Accepted Answer

A)  3.5456 
B)  3.4856 
C)  3.4456 
D)  3.5156 
E)  3.5656 
A)  3.5456 
B)  3.4856 
C)  3.4456 
D)  3.5156 
E)  3.5656

Question 10

Assume that   ,   , and   . Use these values and the properties of logarithms to find the value. Do not use a calculator.

Accepted Answer

A)  3.1661 
B)  2.2588 
C)  1.3929 
D)  2.1583 
E)  2.5814 
A)  3.1661 
B)  2.2588 
C)  1.3929 
D)  2.1583 
E)  2.5814

Question 11

Assume that   ,   , and   . Use these values and the properties of logarithms to find the value. Do not use a calculator.

Accepted Answer

A)  1.4905 
B)  2.3978 
C)  3.2637 
D)  2.4983 
E)  2.9214 
A)  1.4905 
B)  2.3978 
C)  3.2637 
D)  2.4983 
E)  2.9214

Question 12

Assume that   ,   ,   , and     are positive numbers. Use the properties of logarithms to write the expression in terms of the logarithms of   ,   , and   .

Accepted Answer

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

Question 13

Assume that x , y , and b ( b ≠ 1) are positive numbers. Use the properties of logarithms to write the expression in terms of the logarithms of x and y .

Accepted Answer

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

Question 14

Use the properties of logarithms to write   as the logarithm of a single quantity. Assume x and y are positive numbers.

Accepted Answer

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

Question 15

An initial deposit of $26,000 grows at an annual rate of 7% for 20 years. Compare the final balances resulting from continuous compounding and annual compounding. Round the answers to the nearest cent.

Accepted Answer

A)  $100,610.89 from annual compounding; $105,433.70 from continuous compounding 
B)  $100,611.80 from annual compounding; $105,435.20 from continuous compounding 
C)  $100,613.85 from annual compounding; $105,455.20 from continuous compounding 
D)  $100,608.80 from annual compounding; $105,437.25 from continuous compounding 
A)  $100,610.89 from annual compounding; $105,433.70 from continuous compounding 
B)  $100,611.80 from annual compounding; $105,435.20 from continuous compounding 
C)  $100,613.85 from annual compounding; $105,455.20 from continuous compounding 
D)  $100,608.80 from annual compounding; $105,437.25 from continuous compounding

Question 16

Solve the logarithmic equation. Check the solution.

Accepted Answer

A)  x = 5 
B)  x = 4 
C)  x = 7 
D)  x = 6 
A)  x = 5 
B)  x = 4 
C)  x = 7 
D)  x = 6

Question 17

How long will it take $1,500 to double itself if it is invested at 5% interest compounded semiannually? Please round the answer to the nearest tenth.

Accepted Answer

A)  14.0 years 
B)  17.0 years 
C)  14.5 years 
D)  13.0 years 
E)  15.0 years 
A)  14.0 years 
B)  17.0 years 
C)  14.5 years 
D)  13.0 years 
E)  15.0 years

Question 18

Assume that   ,   ,   , and     are positive numbers.Use the properties of logarithms to write the expression in terms of the logarithms of x , y , and z .

Accepted Answer

A)  log b  x log b  y log b  z 
B)  log b  x + log b  y + log b  z 
C)  - log b  x - log b  y - log b  z 
D)  log b  x - log b  y - log b  z 
A)  log b  x log b  y log b  z 
B)  log b  x + log b  y + log b  z 
C)  - log b  x - log b  y - log b  z 
D)  log b  x - log b  y - log b  z

Question 19

Use a calculator to find each common logarithm. Express answer to four decimal places.

Accepted Answer

A)  0.8579 
B)  0.9579 
C)  0.8779 
D)  1.3579 
E)  0.8279 
A)  0.8579 
B)  0.9579 
C)  0.8779 
D)  1.3579 
E)  0.8279

Question 20

Find the dB gain of an amplifier if the output voltage is 30 volts when the input voltage is 0.6 volt. Round your answer to the nearest hundredth.

Accepted Answer

A)  3.00 dB 
B)  49.24 dB 
C)  1.70 dB 
D)  33.98 dB 
E)  None of these 
A)  3.00 dB 
B)  49.24 dB 
C)  1.70 dB 
D)  33.98 dB 
E)  None of these

Graph the function . Remember that the graph of is given.

Solve the logarithmic equation. Check the solution.

Assume that and . Use the change-of-base formula to find the logarithm to four decimal places.

Find the value, if possible. Give the answer to four decimal places.

A piece of machinery valued at $38,000 depreciates at a rate of 7% yearly. How long will it take until it has a value of $19,000? Please round the answer to the nearest tenth.

Solve the exponential equation and express solution to the nearest hundredth.

How long will it take $800 to double itself if it is invested at 5% interest compounded semiannually? Please round the answer to the nearest tenth.

Use a calculator to find each common logarithm. Express answer to four decimal places.

Assume that , , and . Use these values and the properties of logarithms to find the value. Do not use a calculator.

Assume that , , and . Use these values and the properties of logarithms to find the value. Do not use a calculator.

Assume that , , , and are positive numbers. Use the properties of logarithms to write the expression in terms of the logarithms of , , and .

Assume that x , y , and b ( b ≠ 1) are positive numbers. Use the properties of logarithms to write the expression in terms of the logarithms of x and y .

Use the properties of logarithms to write as the logarithm of a single quantity. Assume x and y are positive numbers.

An initial deposit of $26,000 grows at an annual rate of 7% for 20 years. Compare the final balances resulting from continuous compounding and annual compounding. Round the answers to the nearest cent.

Solve the logarithmic equation. Check the solution.

How long will it take $1,500 to double itself if it is invested at 5% interest compounded semiannually? Please round the answer to the nearest tenth.

Assume that , , , and are positive numbers.Use the properties of logarithms to write the expression in terms of the logarithms of x , y , and z .

Use a calculator to find each common logarithm. Express answer to four decimal places.

Find the dB gain of an amplifier if the output voltage is 30 volts when the input voltage is 0.6 volt. Round your answer to the nearest hundredth.

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Linear Equations

Inequalities

Polynomials, Polynomial Functions, and Equations

Rational Expressions

Radical Expressions and Equations

Quadratic Equations and Functions; Inequalities; and Algebra, Composition, and Inverses of Functions

Conic Sections and More Graphing

Miscellaneous Topics

Filters

Exam 9: Exponential and Logarithmic Functions

Graph the function . Remember that the graph of is given.

Solve the logarithmic equation. Check the solution.

Assume that and . Use the change-of-base formula to find the logarithm to four decimal places.

Find the value, if possible. Give the answer to four decimal places.

A piece of machinery valued at $38,000 depreciates at a rate of 7% yearly. How long will it take until it has a value of $19,000? Please round the answer to the nearest tenth.

Solve the exponential equation and express solution to the nearest hundredth.

How long will it take $800 to double itself if it is invested at 5% interest compounded semiannually? Please round the answer to the nearest tenth.

Use a calculator to find each common logarithm. Express answer to four decimal places.

Assume that , , and . Use these values and the properties of logarithms to find the value. Do not use a calculator.

Assume that , , and . Use these values and the properties of logarithms to find the value. Do not use a calculator.

Assume that , , , and are positive numbers. Use the properties of logarithms to write the expression in terms of the logarithms of , , and .

Assume that x , y , and b ( b ≠ 1) are positive numbers. Use the properties of logarithms to write the expression in terms of the logarithms of x and y .

Use the properties of logarithms to write as the logarithm of a single quantity. Assume x and y are positive numbers.

An initial deposit of $26,000 grows at an annual rate of 7% for 20 years. Compare the final balances resulting from continuous compounding and annual compounding. Round the answers to the nearest cent.

Solve the logarithmic equation. Check the solution.

How long will it take $1,500 to double itself if it is invested at 5% interest compounded semiannually? Please round the answer to the nearest tenth.

Assume that , , , and are positive numbers.Use the properties of logarithms to write the expression in terms of the logarithms of x , y , and z .

Use a calculator to find each common logarithm. Express answer to four decimal places.

Find the dB gain of an amplifier if the output voltage is 30 volts when the input voltage is 0.6 volt. Round your answer to the nearest hundredth.

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Linear Equations

Inequalities

Polynomials, Polynomial Functions, and Equations

Rational Expressions

Radical Expressions and Equations

Quadratic Equations and Functions; Inequalities; and Algebra, Composition, and Inverses of Functions

Conic Sections and More Graphing

Miscellaneous Topics

Filters