Question 1

Solve the problem.
-How many times more intense is an earthquake that measures 6.1 on the Richter scale than one that measures 3.4?

Accepted Answer

A) 2.7 
B) 27 
C) 501.187234 
D) 1,258,925.41 
A) 2.7 
B) 27 
C) 501.187234 
D) 1,258,925.41

Question 2

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

Accepted Answer

A) 8 
B) 6 
C) 5 
D) 9 
A) 8 
B) 6 
C) 5 
D) 9

Question 3

Write as a logarithm of a single expression.
-$\log _ { 6 } 13 - \log _ { 6 } 11$

Accepted Answer

A)  $\log _ { 6 } \frac { 13 } { 11 }$ 
B)  $\log _ { 6 } 143$ 
C)  $\frac { \log _ { 6 } 13 } { \log _ { 6 } 11 }$ 
D)  $\log _ { 6 } 2$ 
A)  $\log _ { 6 } \frac { 13 } { 11 }$ 
B)  $\log _ { 6 } 143$ 
C)  $\frac { \log _ { 6 } 13 } { \log _ { 6 } 11 }$ 
D)  $\log _ { 6 } 2$

Question 4

Solve the equation.
-$$\ln ( 10 + 2 x ) = 2 \ln ( x + 1 )$$

Accepted Answer

A) -3 
B) 3 
C) 3, -3 
D)  $\frac { 8 } { 0 }$ 
A) -3 
B) 3 
C) 3, -3 
D)  $\frac { 8 } { 0 }$

Question 5

Write as a logarithm of a single expression.
-$\frac { 1 } { 6 } \log _ { 7 } 3$

Accepted Answer

A)  $\log _ { 7 } \sqrt [ 3 ] { 6 }$ 
B)  $\log _ { 7 } \frac { \sqrt { 3 } } { 6 }$ 
C)  $\log _ { 7 } \frac { 3 } { \sqrt { 6 } }$ 
D)  $\log _ { 7 } \sqrt [ 6 ] { 3 }$ 
A)  $\log _ { 7 } \sqrt [ 3 ] { 6 }$ 
B)  $\log _ { 7 } \frac { \sqrt { 3 } } { 6 }$ 
C)  $\log _ { 7 } \frac { 3 } { \sqrt { 6 } }$ 
D)  $\log _ { 7 } \sqrt [ 6 ] { 3 }$

Question 6

Use the change of base formula to find the value of the following logarithm. Do not round logarithms in the change of
base formula. Write the answer rounded to the nearest ten-thousandth.
-$$\log _ { 5 } 2$$

Accepted Answer

A) -0.3979 
B) 2.3219 
C) 0.4307 
D) 1.0000 
A) -0.3979 
B) 2.3219 
C) 0.4307 
D) 1.0000

Question 7

Use properties of logarithms to expand the logarithmic expression as much as possible.
-$\log _ { 4 } \frac { \sqrt [ 7 ] { 9 } } { s ^ { 2 } r }$

Accepted Answer

A)  $\frac { 1 } { 7 } \log _ { 4 } 9 - 2 \log _ { 4 } s - 2 \log _ { 4 } r$ 
B)  $\frac { 1 } { 7 } \log _ { 4 } 9 - 2 \log _ { 4 } s - \log _ { 4 } r$ 
C)  $7 \log _ { 4 } 9 - 2 \log _ { 4 } s - \log _ { 4 } 7$ 
D)  $\log _ { 4 } 9 - \log _ { 4 } s - \log _ { 4 } r$ 
A)  $\frac { 1 } { 7 } \log _ { 4 } 9 - 2 \log _ { 4 } s - 2 \log _ { 4 } r$ 
B)  $\frac { 1 } { 7 } \log _ { 4 } 9 - 2 \log _ { 4 } s - \log _ { 4 } r$ 
C)  $7 \log _ { 4 } 9 - 2 \log _ { 4 } s - \log _ { 4 } 7$ 
D)  $\log _ { 4 } 9 - \log _ { 4 } s - \log _ { 4 } r$

Question 8

Solve the equation without using a calculator.
-13 x = 271

Accepted Answer

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

Question 9

Find the number N. Round N to six decimal places.
-log N = -2.5554

Accepted Answer

A) 12.876449 
B) 0.555213 
C) 0.002784 
D) 359.252666 
A) 12.876449 
B) 0.555213 
C) 0.002784 
D) 359.252666

Question 10

Evaluate.
-$\log _ { 8 } \frac { 1 } { 64 }$

Accepted Answer

A) -8 
B) -2 
C) 8 
D) 2 
A) -8 
B) -2 
C) 8 
D) 2

Question 11

Find the common logarithm of the number. Round answer to four decimal places.
-log 237

Accepted Answer

A) 2.3766 
B) 5.4681 
C) 2.3729 
D) 2.3747 
A) 2.3766 
B) 5.4681 
C) 2.3729 
D) 2.3747

Question 12

Evaluate.
-$\left( 3 ^ { 2 } \right) ^ { \log_ 98 }$

Accepted Answer

A) 8 
B) 16 
C) 6561 
D) 24 
A) 8 
B) 16 
C) 6561 
D) 24

Question 13

Determine whether the function is a one-to-one function.
-$$y = x ^ { 2 } + 4 x + 11$$

Accepted Answer

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

Question 14

Find the antilog of the logarithm. Round the answer to six decimal places.
-0.3716

Accepted Answer

A) 1.089331 
B) 0.425011 
C) 0.689630 
D) 2.352881 
A) 1.089331 
B) 0.425011 
C) 0.689630 
D) 2.352881

Question 15

Find the number N. Round N to six decimal places.
-log N = 0.9387

Accepted Answer

A) 1.241281 
B) 0.391136 
C) 0.115160 
D) 8.683604 
A) 1.241281 
B) 0.391136 
C) 0.115160 
D) 8.683604

Question 16

Solve the equation without using a calculator.
-$3 ^ { - x } = 27$

Accepted Answer

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

Question 17

By changing the logarithm to exponential form, evaluate the common logarithm without the use of a calculator.
-log 100

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B) 20 
C) 2 
D)  $\frac { 1 } { 5 }$ 
A)  $\frac { 1 } { 2 }$ 
B) 20 
C) 2 
D)  $\frac { 1 } { 5 }$

Question 18

Write as a logarithm of a single expression.
-$\frac { 1 } { 2 } \left( \log _ { 6 } ( r - 3 ) - \log _ { 6 } r \right)$

Accepted Answer

A)  $\log _ { 6 } \frac { r - 3 } { \sqrt { r } }$ 
B)  $\log _ { 6 } \frac { \sqrt { r - 3 } } { r }$ 
C)  $\log _ { 6 } \sqrt { \frac { r - 3 } { r } }$ 
D)  $\log _ { 6 } \sqrt { \frac { r - 3 } { 2 r } }$ 
A)  $\log _ { 6 } \frac { r - 3 } { \sqrt { r } }$ 
B)  $\log _ { 6 } \frac { \sqrt { r - 3 } } { r }$ 
C)  $\log _ { 6 } \sqrt { \frac { r - 3 } { r } }$ 
D)  $\log _ { 6 } \sqrt { \frac { r - 3 } { 2 r } }$

Question 19

Solve the equation without using a calculator.
-$$4 ^ { ( 3 x - 7 ) } = 16$$

Accepted Answer

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

Question 20

For the given functions f and g , find the indicated composition.
-$$\begin{array} { l } 
f ( x ) = 3 x + 13 , \quad g ( x ) = 5 x - 1 \
( f \circ g ) ( x )
\end{array}$$

Accepted Answer

A) 15x + 12 
B) 15x + 10 
C) 15x + 16 
D) 15x + 64 
A) 15x + 12 
B) 15x + 10 
C) 15x + 16 
D) 15x + 64

Solve the problem. -How many times more intense is an earthquake that measures 6.1 on the Richter scale than one that measures 3.4?

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

Write as a logarithm of a single expression. - $\log _ { 6 } 13 - \log _ { 6 } 11$

Solve the equation. - $\ln ( 10 + 2 x ) = 2 \ln ( x + 1 )$

Write as a logarithm of a single expression. - $\frac { 1 } { 6 } \log _ { 7 } 3$

Use the change of base formula to find the value of the following logarithm. Do not round logarithms in the change of base formula. Write the answer rounded to the nearest ten-thousandth. - $\log _ { 5 } 2$

Use properties of logarithms to expand the logarithmic expression as much as possible. - $\log _ { 4 } \frac { \sqrt [ 7 ] { 9 } } { s ^ { 2 } r }$

Solve the equation without using a calculator. -13 x = 271

Find the number N. Round N to six decimal places. -log N = -2.5554

Evaluate. - $\log _ { 8 } \frac { 1 } { 64 }$

Find the common logarithm of the number. Round answer to four decimal places. -log 237

Evaluate. - $\left( 3 ^ { 2 } \right) ^ { \log_ 98 }$

Determine whether the function is a one-to-one function. - $y = x ^ { 2 } + 4 x + 11$

Find the antilog of the logarithm. Round the answer to six decimal places. -0.3716

Find the number N. Round N to six decimal places. -log N = 0.9387

Solve the equation without using a calculator. - $3 ^ { - x } = 27$

By changing the logarithm to exponential form, evaluate the common logarithm without the use of a calculator. -log 100

Write as a logarithm of a single expression. - $\frac { 1 } { 2 } \left( \log _ { 6 } ( r - 3 ) - \log _ { 6 } r \right)$

Solve the equation without using a calculator. - $4 ^ { ( 3 x - 7 ) } = 16$

For the given functions f and g , find the indicated composition. - f(x)=3x+13,g(x)=5x-1 (f\circg)(x)

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