Question 1

Find the domain of the logarithmic function.
-$$f ( x ) = \log _ { 6 } ( x + 9 ) ^ { 2 }$$

Accepted Answer

A)  $( - \infty , - 9 )$ or $( - 9 , \infty )$ 
B)  $( - \infty , 0 )$ or $( 0 , \infty )$ 
C)  $( - 9 , \infty )$ 
D)  $( 9 , \infty )$ (9 
A)  $( - \infty , - 9 )$ or $( - 9 , \infty )$ 
B)  $( - \infty , 0 )$ or $( 0 , \infty )$ 
C)  $( - 9 , \infty )$ 
D)  $( 9 , \infty )$ (9

Question 2

Use the Power Rule
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$$\log _ { 4 } \sqrt [ 3 ] { y }$$

Accepted Answer

A)  $\frac { 1 } { 3 } \log _ { 4 } y$ 
B)  $\frac { 1 } { 4 } \log _ { 3 } y$ 
C)  $\frac { 1 } { 3 } \log _ { 4 } \sqrt [ 3 ] { y }$ 
D)  $3 \log _ { 4 } y$ 
A)  $\frac { 1 } { 3 } \log _ { 4 } y$ 
B)  $\frac { 1 } { 4 } \log _ { 3 } y$ 
C)  $\frac { 1 } { 3 } \log _ { 4 } \sqrt [ 3 ] { y }$ 
D)  $3 \log _ { 4 } y$

Question 3

Write the equation in its equivalent logarithmic form.
-$$72 = x$$

Accepted Answer

A)  $\log _ { 7 } x = 2$ 
B)  $\log _ { x } 7 = 2$ 
C)  $\log _ { 2 } x = 7$ 
D)  $\log _ { 7 } 2 = x$ 
A)  $\log _ { 7 } x = 2$ 
B)  $\log _ { x } 7 = 2$ 
C)  $\log _ { 2 } x = 7$ 
D)  $\log _ { 7 } 2 = x$

Question 4

Evaluate or simplify the expression without using a calculator.
-$\log 10 ^ { 5 }$

Accepted Answer

A)  5 
B)  10 
C)  $\log 5$ 
D)  $10 ^ { 5 }$ 
A)  5 
B)  10 
C)  $\log 5$ 
D)  $10 ^ { 5 }$

Question 5

Graph the function.
-$$\text { Use the graph of } f ( x ) = e ^ { x } \text { to obtain the graph of } g ( x ) = e ^ { x } - 4$$

Accepted Answer

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

Question 6

Solve the problem.
-The formula $S = A \left( \frac { ( 1 + r ) ^ { t } + 1 - 1 } { r } \right)$ models the value of a retirement account, where $A =$ the number of dollars added to the retirement account each year, $\mathrm { r } =$ the annual interest rate, and $\mathrm { S } =$ the value of the retirement account after t years. If the interest rate is $7 \%$, how much will the account be worth after 15 years if $\$ 800$ is added each year? Round to the nearest whole number.

Accepted Answer

A)  $\$ 22,310$ 
B)  $\$ 2347$ 
C)  $\$ 12,800$ 
D)  $\$ 35,316$ 
A)  $\$ 22,310$ 
B)  $\$ 2347$ 
C)  $\$ 12,800$ 
D)  $\$ 35,316$

Question 7

Evaluate or simplify the expression without using a calculator.
-$\log 1000$

Accepted Answer

A)  3 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 3 } { 10 }$ 
D)  30 
A)  3 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 3 } { 10 }$ 
D)  30

Question 8

Evaluate or simplify the expression without using a calculator.
-$\log 0.01$

Accepted Answer

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

Question 9

Use Natural Logarithms
Evaluate or simplify the expression without using a calculator.
-$\ln \mathrm { e }$

Accepted Answer

A)  1 
B)  0 
C)  $\mathrm { e }$ 
D)  $- 1$ 
A)  1 
B)  0 
C)  $\mathrm { e }$ 
D)  $- 1$

Question 10

Graph the function by making a table of coordinates.
-$$f ( x ) = 0.2 ^ { x }$$

Accepted Answer

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

Question 11

Use the One-to-One Property of Logarithms to Solve Logarithmic Equations
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic
expressions. Give the exact answer.
-$\log ( x + 24 ) - \log 4 = \log ( 7 x + 3 )$

Accepted Answer

A)  $\left\{ \frac { 4 } { 9 } \right\}$ 
B)  $\{ 31 \}$ 
C)  $\left\{ - \frac { 4 } { 9 } \right\}$ 
D)  $\{ - 31 \}$ 
A)  $\left\{ \frac { 4 } { 9 } \right\}$ 
B)  $\{ 31 \}$ 
C)  $\left\{ - \frac { 4 } { 9 } \right\}$ 
D)  $\{ - 31 \}$

Question 12

Evaluate the expression without using a calculator.
-$\log _ { 8 } 8 ^ { 19 }$

Accepted Answer

A)  19 
B)  8 
C)  27 
D)  $\log _ { 8 } 19$ 
A)  19 
B)  8 
C)  27 
D)  $\log _ { 8 } 19$

Question 13

Use Compound Interest Formulas
Use the compound interest formulas A $$A = P \left( 1 + \frac { r } { n } \right) \text { and } A = P e ^ { r t } \text { to solve }$$
-Find the accumulated value of an investment of $5000 at 5% compounded monthly for 8 years.

Accepted Answer

A) $7452.93 
B) $12,911.25 
C) $9093.60 
D) $8060.16 
A) $7452.93 
B) $12,911.25 
C) $9093.60 
D) $8060.16

Question 14

Model Exponential Growth and Decay
Solve.
-A fossilized leaf contains 18% of its normal amount of carbon 14. How old is the fossil (to the nearest year)? Use 5600 years as the half-life of carbon 14.

Accepted Answer

A) 13,829 
B) 23,309 
C) 1600 
D) 35,538 
A) 13,829 
B) 23,309 
C) 1600 
D) 35,538

Question 15

Use the One-to-One Property of Logarithms to Solve Logarithmic Equations
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic
expressions. Give the exact answer.
-$\log ( x + 4 ) = \log ( 4 x + 1 )$

Accepted Answer

A)  $\{ 1 \}$ 
B)  $\left\{ \frac { 3 } { 5 } \right\}$ 
C)  $\{ - 1 \}$ 
D)  $\left\{ \frac { 1 } { 3 } \right\}$ 
A)  $\{ 1 \}$ 
B)  $\left\{ \frac { 3 } { 5 } \right\}$ 
C)  $\{ - 1 \}$ 
D)  $\left\{ \frac { 1 } { 3 } \right\}$

Question 16

Approximate the number using a calculator. Round your answer to three decimal places.
-$3.2 \pi$

Accepted Answer

A)  $38.635$ 
B)  $38.983$ 
C)  $10.053$ 
D)  $36.462$ 
A)  $38.635$ 
B)  $38.983$ 
C)  $10.053$ 
D)  $36.462$

Question 17

Solve the problem.
-If Emery has $1200 to invest at 8% per year compounded monthly, how long will it be before he has $2400? If the compounding is continuous, how long will it be? (Round your answers to three decimal
Places.)

Accepted Answer

A) 8.693 yrs, 8.664 yrs 
B) 0.751 yrs, 0.722 yrs 
C) 80.889 yrs, 8.914 yrs 
D) 0.113 yrs, 0.866 yrs 
A) 8.693 yrs, 8.664 yrs 
B) 0.751 yrs, 0.722 yrs 
C) 80.889 yrs, 8.914 yrs 
D) 0.113 yrs, 0.866 yrs

Question 18

Use the One-to-One Property of Logarithms to Solve Logarithmic Equations
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic
expressions. Give the exact answer.
-$$\ln ( x - 6 ) + \ln ( x + 1 ) = \ln ( x - 15 )$$

Accepted Answer

A)  $\{ - 3 \}$ 
B)  $\{ 3 \}$ 
C)  $\{ 3 , - 3 \}$ 
D)  $\varnothing$ 
A)  $\{ - 3 \}$ 
B)  $\{ 3 \}$ 
C)  $\{ 3 , - 3 \}$ 
D)  $\varnothing$

Question 19

Model Exponential Growth and Decay
Solve.
-The population of a certain country is growing at a rate of $2.6 \%$ per year. How long will it take for this country's population to double? Use the formula $t = \frac { \ln 2 } { k }$, which gives the time, $t$, for a population with growth rate k, to double. (Round to the nearest whole year.)

Accepted Answer

A)  27 years 
B)  28 years 
C)  29 years 
D)  26 years 
A)  27 years 
B)  28 years 
C)  29 years 
D)  26 years

Question 20

Evaluate or simplify the expression without using a calculator.
-$\log \left( \frac { 1 } { 10,000 } \right)$

Accepted Answer

A)  $- 4$ 
B)  4 
C)  $\frac { 1 } { 10,000 }$ 
D)  $- \frac { 1 } { 4 }$ 
A)  $- 4$ 
B)  4 
C)  $\frac { 1 } { 10,000 }$ 
D)  $- \frac { 1 } { 4 }$

Find the domain of the logarithmic function. - $f ( x ) = \log _ { 6 } ( x + 9 ) ^ { 2 }$

Use the Power Rule Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 4 } \sqrt [ 3 ] { y }$

Write the equation in its equivalent logarithmic form. - $72 = x$

Evaluate or simplify the expression without using a calculator. - $\log 10 ^ { 5 }$

Graph the function. - $\text { Use the graph of } f ( x ) = e ^ { x } \text { to obtain the graph of } g ( x ) = e ^ { x } - 4$ $Graph the function. - \text { Use the graph of } f ( x ) = e ^ { x } \text { to obtain the graph of } g ( x ) = e ^ { x } - 4$

Evaluate or simplify the expression without using a calculator. - $\log 1000$

Evaluate or simplify the expression without using a calculator. - $\log 0.01$

Use Natural Logarithms Evaluate or simplify the expression without using a calculator. - $\ln \mathrm { e }$

Graph the function by making a table of coordinates. - $f ( x ) = 0.2 ^ { x }$ $Graph the function by making a table of coordinates. - f ( x ) = 0.2 ^ { x }$

Use the One-to-One Property of Logarithms to Solve Logarithmic Equations Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. - $\log ( x + 24 ) - \log 4 = \log ( 7 x + 3 )$

Evaluate the expression without using a calculator. - $\log _ { 8 } 8 ^ { 19 }$

Use Compound Interest Formulas Use the compound interest formulas A $A = P \left( 1 + \frac { r } { n } \right) \text { and } A = P e ^ { r t } \text { to solve }$ -Find the accumulated value of an investment of $5000 at 5% compounded monthly for 8 years.

Model Exponential Growth and Decay Solve. -A fossilized leaf contains 18% of its normal amount of carbon 14. How old is the fossil (to the nearest year)? Use 5600 years as the half-life of carbon 14.

Use the One-to-One Property of Logarithms to Solve Logarithmic Equations Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. - $\log ( x + 4 ) = \log ( 4 x + 1 )$

Approximate the number using a calculator. Round your answer to three decimal places. - $3.2 \pi$

Solve the problem. -If Emery has $1200 to invest at 8% per year compounded monthly, how long will it be before he has $2400? If the compounding is continuous, how long will it be? (Round your answers to three decimal Places.)

Use the One-to-One Property of Logarithms to Solve Logarithmic Equations Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. - $\ln ( x - 6 ) + \ln ( x + 1 ) = \ln ( x - 15 )$

Evaluate or simplify the expression without using a calculator. - $\log \left( \frac { 1 } { 10,000 } \right)$

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Exam 4: Exponential and Logarithmic Functions

Find the domain of the logarithmic function. - f(x)=log⁡6(x+9)2f ( x ) = \log _ { 6 } ( x + 9 ) ^ { 2 }f(x)=log6​(x+9)2

Use the Power Rule Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡4y3\log _ { 4 } \sqrt [ 3 ] { y }log4​3y​

Write the equation in its equivalent logarithmic form. - 72=x72 = x72=x

Evaluate or simplify the expression without using a calculator. - log⁡105\log 10 ^ { 5 }log105

Graph the function. - Use the graph of f(x)=ex to obtain the graph of g(x)=ex−4\text { Use the graph of } f ( x ) = e ^ { x } \text { to obtain the graph of } g ( x ) = e ^ { x } - 4 Use the graph of f(x)=ex to obtain the graph of g(x)=ex−4

Evaluate or simplify the expression without using a calculator. - log⁡1000\log 1000log1000

Evaluate or simplify the expression without using a calculator. - log⁡0.01\log 0.01log0.01

Use Natural Logarithms Evaluate or simplify the expression without using a calculator. - ln⁡e\ln \mathrm { e }lne

Graph the function by making a table of coordinates. - f(x)=0.2xf ( x ) = 0.2 ^ { x }f(x)=0.2x

Evaluate the expression without using a calculator. - log⁡8819\log _ { 8 } 8 ^ { 19 }log8​819