Question 1

Use the properties of logarithms to evaluate the expression without the use of a calculator.
-$$4 ^ { \log _ { 4 } 6 }$$

Accepted Answer

A) 1 
B) 6 
C) 4 
D) 24 
A) 1 
B) 6 
C) 4 
D) 24

Question 2

Solve the problem.
-Sandy manages a ceramics shop and uses a 650°F kiln to fire ceramic greenware. After turning off her kiln, she must wait until its temperature gauge reaches 180°F before opening it and removing the ceramic pieces. If room temperature is 70°F and the gauge reads 550°F in 10 minutes, how long must she wait before opening the kiln? Round your answer to the nearest whole minute.

Accepted Answer

A) 59 min 
B) 313 min 
C) 220 min 
D) 88 min 
A) 59 min 
B) 313 min 
C) 220 min 
D) 88 min

Question 3

Write the logarithmic equation as an exponential equation.
-$\log _ { b } 36 = 2$

Accepted Answer

A)  $2 ^ { b } = 36$ 
B)  $36 ^ { 2 } = b$ 
C)  $b ^ { 2 } = 36$ 
D)  $36 ^ { b } = 2$ 
A)  $2 ^ { b } = 36$ 
B)  $36 ^ { 2 } = b$ 
C)  $b ^ { 2 } = 36$ 
D)  $36 ^ { b } = 2$

Question 4

Solve the problem.
-$$f ( t ) = \frac { 20,000 } { 1 + 399 \mathrm { e } ^ { - 1.4 t } }$$ particular infection t weeks after its initial outbreak in a particular community. How many people were ill after 5 weeks?

Accepted Answer

A) 20,400 people 
B) 14,664 people 
C) 250 people 
D) 20,000 people 
A) 20,400 people 
B) 14,664 people 
C) 250 people 
D) 20,000 people

Question 5

Solve the problem.
-A thermometer reading 37°F is brought into a room with a constant temperature of 75°F. If the thermometer reads 45°F after 6 minutes, what will it read after being in the room for 9 minutes? Round your answer to two decimal places.

Accepted Answer

A) 32.86°F 
B) 101.66°F 
C) 70.47°F 
D) 48.34°F 
A) 32.86°F 
B) 101.66°F 
C) 70.47°F 
D) 48.34°F

Question 6

Solve the equation.
-$$5 ^ { x } = 625$$

Accepted Answer

A)  $\{ 4 \}$ 
B)  $\{ 125 \}$ 
C)  $\{ 3 \}$ 
D)  $\{ 5 \}$ 
A)  $\{ 4 \}$ 
B)  $\{ 125 \}$ 
C)  $\{ 3 \}$ 
D)  $\{ 5 \}$

Question 7

Evaluate the expression without the use of a calculator, and then verify your answer using a calculator.
-ln e

Accepted Answer

A) 0 
B) 1 
C) -1 
D) e 
A) 0 
B) 1 
C) -1 
D) e

Question 8

Solve the equation.
-$\log ( x + 4 ) = \log ( 5 x - 5 )$

Accepted Answer

A)  $\left\{ - \frac { 1 } { 4 } \right\}$ 
B)  $\left\{ \frac { 9 } { 4 } \right\}$ 
C)  $\left\{ \frac { 9 } { 5 } \right\}$ 
D)  $\left\{ - \frac { 9 } { 4 } \right\}$ 
A)  $\left\{ - \frac { 1 } { 4 } \right\}$ 
B)  $\left\{ \frac { 9 } { 4 } \right\}$ 
C)  $\left\{ \frac { 9 } { 5 } \right\}$ 
D)  $\left\{ - \frac { 9 } { 4 } \right\}$

Question 9

Graph the function.
-

Accepted Answer

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

Question 10

Solve the problem.
-$$P ( t ) = \frac { 980 } { 1 + 20.78 e ^ { - 0.346 t } }$$ The logistic growth model represents the population of a bacterium in a culture tube after t hours. When will the amount of bacteria be 610?

Accepted Answer

A) 7.4 hr 
B) 4.43 hr 
C) 1.62 hr 
D) 10.21 hr 
A) 7.4 hr 
B) 4.43 hr 
C) 1.62 hr 
D) 10.21 hr

Question 11

Approximate the value using a calculator. Round your answer to three decimal places.
-$$\mathrm { e } ^ { \pi }$$

Accepted Answer

A) 23.141 
B) 22.459 
C) 8.540 
D) 5.860 
A) 23.141 
B) 22.459 
C) 8.540 
D) 5.860

Question 12

Graph the function.
-$$f ( x ) = \log _ { 3 } x + 1$$

Accepted Answer

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

Question 13

Solve the problem.
-The function D(h)= 8e-0.4h can be used to determine the milligrams D of a certain drug in a patient's bloodstream h hours after the drug has been given. How many milligrams (to two decimals)will be present after 12 hours?

Accepted Answer

A) 4.76 mg 
B) 0.07 mg 
C) 972.08 mg 
D) 0.49 mg 
A) 4.76 mg 
B) 0.07 mg 
C) 972.08 mg 
D) 0.49 mg

Question 14

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the
solution.
-$$e ^ { 5 x } = 8$$

Accepted Answer

A)  $\{ 0.42 \}$ 
B)  $\{ 10.40 \}$ 
C)  $\{ 0.20 \}$ 
D)  $\{ 4.35 \}$ 
A)  $\{ 0.42 \}$ 
B)  $\{ 10.40 \}$ 
C)  $\{ 0.20 \}$ 
D)  $\{ 4.35 \}$

Question 15

Solve the equation.
-$$3 \cdot 5 ^ { 2 t - 1}  = 75$$

Accepted Answer

A)  $\{ 3 \}$ 
B)  $\left\{ \frac { 13 } { 10 } \right\}$ 
C)  $\left\{ \frac { 3 } { 2 } \right\}$ 
D)  $\left\{ \frac { 1 } { 2 } \right\}$ 
A)  $\{ 3 \}$ 
B)  $\left\{ \frac { 13 } { 10 } \right\}$ 
C)  $\left\{ \frac { 3 } { 2 } \right\}$ 
D)  $\left\{ \frac { 1 } { 2 } \right\}$

Question 16

Approximate the value using a calculator. Round your answer to three decimal places.
-$$e ^ { - 1.1 }$$

Accepted Answer

A) 0.633 
B) -2.990 
C) -0.333 
D) 0.333 
A) 0.633 
B) -2.990 
C) -0.333 
D) 0.333

Question 17

Use the change of base formula and a calculator to evaluate the logarithm. Round your answer to two decimal places.
-$\log _ { 6.5 } 4.2$

Accepted Answer

A)  $1.30$ 
B)  $0.62$ 
C)  $0.65$ 
D)  $0.77$ 
A)  $1.30$ 
B)  $0.62$ 
C)  $0.65$ 
D)  $0.77$

Question 18

Evaluate the expression without the use of a calculator, and then verify your answer using a calculator.
-$$\ln \mathrm { e } ^ { 10 }$$

Accepted Answer

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

Question 19

Determine the correct exponential function of the form f(x) = bS1U1P1xS1S1P0 whose graph is given.
-

Accepted Answer

A)  $f ( x ) = 5 ^ { x }$ 
B)  $f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x }$ 
C)  $f ( x ) = \left( \frac { 1 } { 5 } \right) ^ { x }$ 
D)  $f ( x ) = 2 ^ { x }$ 
A)  $f ( x ) = 5 ^ { x }$ 
B)  $f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x }$ 
C)  $f ( x ) = \left( \frac { 1 } { 5 } \right) ^ { x }$ 
D)  $f ( x ) = 2 ^ { x }$

Question 20

Use the change of base formula and the properties of logarithms to rewrite the expression as a single logarithm in the
indicated base.
-$\log 81 x ^ { 12 } + \log 27 y ^ { 9 } - \log _ { 9 } w ^ { 6 }$, base 3

Accepted Answer

A)  $\log _ { 3 } \frac { x ^ { 12 } y ^ { 9 } } { z ^ { 6 } }$ 
B)  $\log _ { 3 } \frac { x ^ { 3 } y ^ { 3 } } { z ^ { 3 } }$ 
C)  $\log _ { 3 } \left( x ^ { 3 } + y ^ { 3 } - z ^ { 3 } \right)$ 
D)  $\log _ { 3 } x ^ { 3 } y ^ { 3 } z ^ { 3 }$ 
A)  $\log _ { 3 } \frac { x ^ { 12 } y ^ { 9 } } { z ^ { 6 } }$ 
B)  $\log _ { 3 } \frac { x ^ { 3 } y ^ { 3 } } { z ^ { 3 } }$ 
C)  $\log _ { 3 } \left( x ^ { 3 } + y ^ { 3 } - z ^ { 3 } \right)$ 
D)  $\log _ { 3 } x ^ { 3 } y ^ { 3 } z ^ { 3 }$

Use the properties of logarithms to evaluate the expression without the use of a calculator. - $4 ^ { \log _ { 4 } 6 }$

Write the logarithmic equation as an exponential equation. - $\log _ { b } 36 = 2$

Solve the problem. - $f ( t ) = \frac { 20,000 } { 1 + 399 \mathrm { e } ^ { - 1.4 t } }$ particular infection t weeks after its initial outbreak in a particular community. How many people were ill after 5 weeks?

Solve the problem. -A thermometer reading 37°F is brought into a room with a constant temperature of 75°F. If the thermometer reads 45°F after 6 minutes, what will it read after being in the room for 9 minutes? Round your answer to two decimal places.

Solve the equation. - $5 ^ { x } = 625$

Evaluate the expression without the use of a calculator, and then verify your answer using a calculator. -ln e

Solve the equation. - $\log ( x + 4 ) = \log ( 5 x - 5 )$

Graph the function. -

Solve the problem. - $P ( t ) = \frac { 980 } { 1 + 20.78 e ^ { - 0.346 t } }$ The logistic growth model represents the population of a bacterium in a culture tube after t hours. When will the amount of bacteria be 610?

Approximate the value using a calculator. Round your answer to three decimal places. - $\mathrm { e } ^ { \pi }$

Graph the function. - $f ( x ) = \log _ { 3 } x + 1$ $Graph the function. - f ( x ) = \log _ { 3 } x + 1$

Solve the problem. -The function D(h)= 8e-0.4h can be used to determine the milligrams D of a certain drug in a patient's bloodstream h hours after the drug has been given. How many milligrams (to two decimals)will be present after 12 hours?

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $e ^ { 5 x } = 8$

Solve the equation. - $3 \cdot 5 ^ { 2 t - 1} = 75$

Approximate the value using a calculator. Round your answer to three decimal places. - $e ^ { - 1.1 }$

Use the change of base formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. - $\log _ { 6.5 } 4.2$

Evaluate the expression without the use of a calculator, and then verify your answer using a calculator. - $\ln \mathrm { e } ^ { 10 }$

Determine the correct exponential function of the form f(x) = b^x whose graph is given. -

Use the change of base formula and the properties of logarithms to rewrite the expression as a single logarithm in the indicated base. - $\log 81 x ^ { 12 } + \log 27 y ^ { 9 } - \log _ { 9 } w ^ { 6 }$ , base 3

Equations, Inequalities, and Applications

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Exam 5: Exponential and Logarithmic Functions and Equations

Use the properties of logarithms to evaluate the expression without the use of a calculator. - 4log⁡464 ^ { \log _ { 4 } 6 }4log4​6

Write the logarithmic equation as an exponential equation. - log⁡b36=2\log _ { b } 36 = 2logb​36=2

Solve the problem. - f(t)=20,0001+399e−1.4tf ( t ) = \frac { 20,000 } { 1 + 399 \mathrm { e } ^ { - 1.4 t } }f(t)=1+399e−1.4t20,000​ particular infection t weeks after its initial outbreak in a particular community. How many people were ill after 5 weeks?