Question 1

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or
reflected.
-

Accepted Answer

A)  $\log _ { 2 } ( x - 1 ) + 1$ 
B)  $\log _ { 2 } ( x + 1 ) + 1$ 
C)  $\log _ { 2 } ( x + 1 ) - 1$ 
D)  $\log _ { 2 } ( x - 1 ) - 1$ 
A)  $\log _ { 2 } ( x - 1 ) + 1$ 
B)  $\log _ { 2 } ( x + 1 ) + 1$ 
C)  $\log _ { 2 } ( x + 1 ) - 1$ 
D)  $\log _ { 2 } ( x - 1 ) - 1$

Question 2

Use properties of logarithms to evaluate the expression.
-$\log _ { 10 } ( 0.0001 ) ^ { 9 }$

Accepted Answer

A)  $\log 6561$ 
B)  $\frac { 1 } { 36 }$ 
C)  $- 6561$ 
D)  $- 36$ 
A)  $\log 6561$ 
B)  $\frac { 1 } { 36 }$ 
C)  $- 6561$ 
D)  $- 36$

Question 3

Decide whether the given functions are inverses.
-

Accepted Answer

A) True 
 B)False

Question 4

Why can't 1 be the base of a logarithmic function?

Accepted Answer

Answers may vary. One possibility: If th

Question 5

$$\text { Explain how the graph of } y = \log _ { 2 } ( x - 5 ) \text { can be obtained from the graph of } y = \log _ { 2 } x \text {. }$$

Accepted Answer

The graph

Question 6

Find the domain and range of the inverse of the given function.
-$$f ( x ) = 5 - x ^ { 2 } ; x \geq 0$$

Accepted Answer

A)  Domain: $( - \infty , 5 ]$; range: range: $[ 0 , \infty )$ 
B)  Domain: all real numbers; range: $[ - 5 , \infty )$ 
C)  Domain and range: all real numbers 
D)  Domain: all real numbers; range: $( - \infty , 5 ]$ 
A)  Domain: $( - \infty , 5 ]$; range: range: $[ 0 , \infty )$ 
B)  Domain: all real numbers; range: $[ - 5 , \infty )$ 
C)  Domain and range: all real numbers 
D)  Domain: all real numbers; range: $( - \infty , 5 ]$

Question 7

Write an equivalent expression in exponential form.
-$\log 53125 = x$

Accepted Answer

A)  {625} 
B)  {5} 
C)  {15,625} 
D)  {3130} 
A)  {625} 
B)  {5} 
C)  {15,625} 
D)  {3130}

Question 8

$$\text { Explain how the graph of } y = \log _ { 2 } \frac { x } { 7 } \text { can be obtained from the graph of } y = \log _ { 2 } x \text {. }$$

Accepted Answer

The graph is shifted

Question 9

Write the algebraic equation which can be used to find the exact solution of log3 $( x - 6 ) + \log _ { 3 } ( x - 1 ) = 2$ .

Accepted Answer

The answer of Write the algebraic equation which can be...

Question 10

Find the value. Give an approximation to four decimal places.
-log 0.0820

Accepted Answer

A)  $- 2.5010$ 
B)  $- 1.0915$ 
C)  $- 1.0809$ 
D)  $- 1.0862$ 
A)  $- 2.5010$ 
B)  $- 1.0915$ 
C)  $- 1.0809$ 
D)  $- 1.0862$

Question 11

Find the domain and range of the inverse of the given function.
-$$f ( x ) = x ^ { 3 } - 2$$

Accepted Answer

A)  Domain: $[ 0 , \infty )$; range: $[ 0 , \infty )$ 
B)  Domain and range: all real numbers 
C)  Domain: all real numbers; range: $[ - 2 , \infty )$ 
D)  Domain: $[ - 2 , \infty )$; range: all real numbers 
A)  Domain: $[ 0 , \infty )$; range: $[ 0 , \infty )$ 
B)  Domain and range: all real numbers 
C)  Domain: all real numbers; range: $[ - 2 , \infty )$ 
D)  Domain: $[ - 2 , \infty )$; range: all real numbers

Question 12

Find the domain and range of the inverse of the given function.
-$$f ( x ) = \sqrt { x - 2 }$$

Accepted Answer

A)  Domain: $[ 0 , \infty )$; range: $[ 2 , \infty )$ 
B)  Domain and range: all real numbers 
C)  Domain: $[ 2 , \infty )$; range: $[ 0 , \infty )$ 
D)  Domain: all real numbers; range: $[ 2 , \infty )$ 
A)  Domain: $[ 0 , \infty )$; range: $[ 2 , \infty )$ 
B)  Domain and range: all real numbers 
C)  Domain: $[ 2 , \infty )$; range: $[ 0 , \infty )$ 
D)  Domain: all real numbers; range: $[ 2 , \infty )$

Question 13

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth.
-$$2 ^ { ( x - 1 ) } = 17$$

Accepted Answer

A)  {9.50} 
B)  {5.09} 
C)  {4.25} 
D)  {3.09} 
A)  {9.50} 
B)  {5.09} 
C)  {4.25} 
D)  {3.09}

Question 14

Evaluate the logarithm.
-$\log _ { 10 } 100$

Accepted Answer

A)  20 
B)  10 
C)  2 
D)  100 
A)  20 
B)  10 
C)  2 
D)  100

Question 15

Solve the following graphically. If necessary, round answers to the nearest thousandth.
-$$\ln ( x - 2 ) = - \sqrt [ 3 ] { x + 1 }$$

Accepted Answer

A)  $\{ 2.2432 \}$ 
B)  $\{ 2.228 \}$ 
C)  $\{ 2.263 \}$ 
D)  $\varnothing$ 
A)  $\{ 2.2432 \}$ 
B)  $\{ 2.228 \}$ 
C)  $\{ 2.263 \}$ 
D)  $\varnothing$

Question 16

In a town whose population is 3000, a disease creates an epidemic. The number N of people infected t days after the disease has begun is given by the function N $$\mathrm { N } ( \mathrm { t } ) = \frac { 3000 } { 1 + 21.5 \cdot \mathrm { e } ^ { - 0.5 \mathrm { t } } }$$ . Find the number infected after 8 days.

Accepted Answer

A)  2154 
B)  2155 
C)  2152 
D)  2150 
A)  2154 
B)  2155 
C)  2152 
D)  2150

Question 17

Solve the equation.
-$$4 ^ { - x } = \frac { 1 } { 16 }$$

Accepted Answer

A)  $\{ 2 \}$ 
B)  $\{ - 2 \}$ 
C)  $\left\{ \frac { 1 } { 2 } \right\}$ 
D)  $\left\{ \frac { 1 } { 4 } \right\}$ 
A)  $\{ 2 \}$ 
B)  $\{ - 2 \}$ 
C)  $\left\{ \frac { 1 } { 2 } \right\}$ 
D)  $\left\{ \frac { 1 } { 4 } \right\}$

Question 18

A lake is stocked with 545 fish of a new variety. The size of the lake, the availability of food, and the number of other fish restrict growth in the lake to a limiting value of 3406. The population of fish in the lake after time t, in
Months, is given by the function P(t) $P ( t ) = \frac { 3406 } { 1 + 5.07 e ^ { - 0.25 t } }$ . After how many months will the population be 2405?

Accepted Answer

A)  7 mo 
B)  12 mo 
C)  17 mo 
D)  10 mo 
A)  7 mo 
B)  12 mo 
C)  17 mo 
D)  10 mo

Question 19

Write an equivalent expression in exponential form.
-$$\log _ { 1 / 2 } ( x + 6 ) = - 7$$

Accepted Answer

A)  128 
B)  140 
C)  122 
D)  134 
A)  128 
B)  140 
C)  122 
D)  134

Question 20

Given $\log _ { 10 } 2 \approx 0.3010 \text { and } \log _ { 10 } 3 \approx 0.4771$ find the logarithm without using a calculator.
-$\log _ { 10 } \left( 18 ^ { 1 / 3 } \right)$

Accepted Answer

A)  0.5187 
B)  0.4184 
C)  1.0787 
D)  0.7782 
A)  0.5187 
B)  0.4184 
C)  1.0787 
D)  0.7782

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or reflected. -

Use properties of logarithms to evaluate the expression. - $\log _ { 10 } ( 0.0001 ) ^ { 9 }$

Decide whether the given functions are inverses. -

Why can't 1 be the base of a logarithmic function?

$\text { Explain how the graph of } y = \log _ { 2 } ( x - 5 ) \text { can be obtained from the graph of } y = \log _ { 2 } x \text {. }$

Find the domain and range of the inverse of the given function. - $f ( x ) = 5 - x ^ { 2 } ; x \geq 0$

Write an equivalent expression in exponential form. - $\log 53125 = x$

$\text { Explain how the graph of } y = \log _ { 2 } \frac { x } { 7 } \text { can be obtained from the graph of } y = \log _ { 2 } x \text {. }$

Write the algebraic equation which can be used to find the exact solution of log3 $( x - 6 ) + \log _ { 3 } ( x - 1 ) = 2$ .

Find the value. Give an approximation to four decimal places. -log 0.0820

Find the domain and range of the inverse of the given function. - $f ( x ) = x ^ { 3 } - 2$

Find the domain and range of the inverse of the given function. - $f ( x ) = \sqrt { x - 2 }$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $2 ^ { ( x - 1 ) } = 17$

Evaluate the logarithm. - $\log _ { 10 } 100$

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $\ln ( x - 2 ) = - \sqrt [ 3 ] { x + 1 }$

Solve the equation. - $4 ^ { - x } = \frac { 1 } { 16 }$

Write an equivalent expression in exponential form. - $\log _ { 1 / 2 } ( x + 6 ) = - 7$

Given $\log _ { 10 } 2 \approx 0.3010 \text { and } \log _ { 10 } 3 \approx 0.4771$ find the logarithm without using a calculator. - $\log _ { 10 } \left( 18 ^ { 1 / 3 } \right)$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 5: Inverse, Exponential, and Logarithmic Functions

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or reflected. -

Use properties of logarithms to evaluate the expression. - log⁡10(0.0001)9\log _ { 10 } ( 0.0001 ) ^ { 9 }log10​(0.0001)9

Decide whether the given functions are inverses. -

Why can't 1 be the base of a logarithmic function?

Find the domain and range of the inverse of the given function. - f(x)=5−x2;x≥0f ( x ) = 5 - x ^ { 2 } ; x \geq 0f(x)=5−x2;x≥0

Write an equivalent expression in exponential form. - log⁡53125=x\log 53125 = xlog53125=x

Write the algebraic equation which can be used to find the exact solution of log3 (x−6)+log⁡3(x−1)=2( x - 6 ) + \log _ { 3 } ( x - 1 ) = 2(x−6)+log3​(x−1)=2 .

Find the value. Give an approximation to four decimal places. -log 0.0820

Find the domain and range of the inverse of the given function. - f(x)=x3−2f ( x ) = x ^ { 3 } - 2f(x)=x3−2

Find the domain and range of the inverse of the given function. - f(x)=x−2f ( x ) = \sqrt { x - 2 }f(x)=x−2​

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - 2(x−1)=172 ^ { ( x - 1 ) } = 172(x−1)=17

Evaluate the logarithm. - log⁡10100\log _ { 10 } 100log10​100

Solve the following graphically. If necessary, round answers to the nearest thousandth. - ln⁡(x−2)=−x+13\ln ( x - 2 ) = - \sqrt [ 3 ] { x + 1 }ln(x−2)=−3x+1​

Solve the equation. - 4−x=1164 ^ { - x } = \frac { 1 } { 16 }4−x=161​

Write an equivalent expression in exponential form. - log⁡1/2(x+6)=−7\log _ { 1 / 2 } ( x + 6 ) = - 7log1/2​(x+6)=−7

Given log⁡102≈0.3010 and log⁡103≈0.4771\log _ { 10 } 2 \approx 0.3010 \text { and } \log _ { 10 } 3 \approx 0.4771log10​2≈0.3010 and log10​3≈0.4771 find the logarithm without using a calculator. - log⁡10(181/3)\log _ { 10 } \left( 18 ^ { 1 / 3 } \right)log10​(181/3)

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Use properties of logarithms to evaluate the expression. - $\log _ { 10 } ( 0.0001 ) ^ { 9 }$

Find the domain and range of the inverse of the given function. - $f ( x ) = 5 - x ^ { 2 } ; x \geq 0$

Write an equivalent expression in exponential form. - $\log 53125 = x$

Write the algebraic equation which can be used to find the exact solution of log3 $( x - 6 ) + \log _ { 3 } ( x - 1 ) = 2$ .

Find the domain and range of the inverse of the given function. - $f ( x ) = x ^ { 3 } - 2$

Find the domain and range of the inverse of the given function. - $f ( x ) = \sqrt { x - 2 }$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $2 ^ { ( x - 1 ) } = 17$

Evaluate the logarithm. - $\log _ { 10 } 100$

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $\ln ( x - 2 ) = - \sqrt [ 3 ] { x + 1 }$

Solve the equation. - $4 ^ { - x } = \frac { 1 } { 16 }$

Write an equivalent expression in exponential form. - $\log _ { 1 / 2 } ( x + 6 ) = - 7$

Given $\log _ { 10 } 2 \approx 0.3010 \text { and } \log _ { 10 } 3 \approx 0.4771$ find the logarithm without using a calculator. - $\log _ { 10 } \left( 18 ^ { 1 / 3 } \right)$