Question 1

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

Accepted Answer

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

Question 2

Solve the equation.
-$$\left( \frac { 1 } { 2 } \right) ^ { x } = 8$$

Accepted Answer

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

Question 3

The graph of a logarithmic function is shown. Select the function which matches the graph.
-  A) $f ( x ) = \log _ { 3 } ( x + 2 )$

Accepted Answer

B)  $f ( x ) = \log _ { 3 } x - 2$ 
C)  $f ( x ) = \log _ { 3 } ( x - 2 )$ 
D)  $f ( x ) = \log _ { 3 } x$ 
B)  $f ( x ) = \log _ { 3 } x - 2$ 
C)  $f ( x ) = \log _ { 3 } ( x - 2 )$ 
D)  $f ( x ) = \log _ { 3 } x$

Question 4

Graph the function.
-$f(x)=-1-\ln x$
  A)

Accepted Answer

B)

C) 
  
D) 
  
B)

C) 
  
D)

Question 5

Decide whether or not the functions are inverses of each other.
-$$f ( x ) = \sqrt { x + 7 } \text {, domain } [ - 7 , \infty ) ; g ( x ) = x ^ { 2 } + 7 , \text { domain } ( - \infty , \infty )$$

Accepted Answer

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

Question 6

Solve the problem.
-A cup of coffee is heated to 194° and is then allowed to cool in a room whose air temperature is 72°. After 11 minutes, the temperature of the cup of coffee is 140°. Find the time needed for the coffee to cool to a temperature
Of 102°. Assume the cooling follows Newton's Law of Cooling: $\mathrm { U } = \mathrm { T } + \left( \mathrm { U } _ { \mathrm { O } } - \mathrm { T } \right) \mathrm { e } ^ { \mathrm { kt } }$ (Round your answer to one decimal place.)

Accepted Answer

A)  15.1 minutes 
B)  29.7 minutes 
C)  41.1 minutes 
D)  26.4 minutes 
A)  15.1 minutes 
B)  29.7 minutes 
C)  41.1 minutes 
D)  26.4 minutes

Question 7

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places.
-$\log _ { ( 2 / 3 ) } 19$

Accepted Answer

The answer of Use the Change-of-Base Formula and a calculator...

Question 8

Solve the problem.
-A thermometer is taken from a room at 71°F to the outdoors where the temperature is 14°F. Determine what the
reading on the thermometer will be after 5 minutes, if the reading drops to 45°F after 1 minute. Assume the
cooling follows Newton's Law of Cooling: $\mathrm { U } = \mathrm { T } + \left( \mathrm { U } _ { \mathrm { O } } - \mathrm { T } \right) \mathrm { e } ^ { \mathrm { kt } }$ (Round your answer to two decimal places.)

Accepted Answer

The answer of Solve the problem.
-A thermometer is taken from...

Question 9

Decide whether or not the functions are inverses of each other.
-$$f ( x ) = 4 x + 16 , g ( x ) = \frac { 1 } { 4 } x - 4$$

Accepted Answer

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

Question 10

Solve the problem.
-Two bacteria are placed in a petri dish. The population will double every day. The formula for the number of bacteria in the dish on day t is $$\mathrm { N } ( \mathrm { t } ) = 2 ( 2 ) ^ { t }$$ where t is the number of days after the two bacteria are placed in the dish. How many bacteria are in the dish
Seven days after the two bacteria are placed in the dish?

Accepted Answer

A)  98 
B)  11 
C)  256 
D)  28 
A)  98 
B)  11 
C)  256 
D)  28

Question 11

Find the exact value of the logarithmic expression.
-$\ln \mathrm { e } ^ { 8 }$

Accepted Answer

A)  $\mathrm { e }$ 
B)  8 
C)  $\frac { 1 } { 8 }$ 
D)  1 
A)  $\mathrm { e }$ 
B)  8 
C)  $\frac { 1 } { 8 }$ 
D)  1

Question 12

Find the domain of the function.
-$$f ( x ) = \ln ( - 4 - x )$$

Accepted Answer

A)  $x  4$ 
C)  $x  - 4$ 
A)  $x  4$ 
C)  $x  - 4$

Question 13

Find the domain of the composite function f $f ^ { \circ } g $
-$$f ( x ) = \sqrt { x - 1 } ; \quad g ( x ) = \frac { 1 } { x - 8 }$$

Accepted Answer

A)  $\{ x \mid x \neq 8 , x \neq 1 \}$ 
B)  $\{ x \mid x \geq 1 , x \neq 8 \}$ 
C)  $\{ x \mid x$ is any real number $\}$ 
D)  $\{ x \mid 8 < x \leq 9 \}$ 
A)  $\{ x \mid x \neq 8 , x \neq 1 \}$ 
B)  $\{ x \mid x \geq 1 , x \neq 8 \}$ 
C)  $\{ x \mid x$ is any real number $\}$ 
D)  $\{ x \mid 8 < x \leq 9 \}$

Question 14

Express as a single logarithm.
-$3 \log _ { 6 } x + 5 \log _ { 6 } ( x - 6 )$

Accepted Answer

A)  $\log _ { 6 } x ( x - 6 )$ 
B)  $\log _ { 6 } x ( x - 6 ) ^ { 15 }$ 
C)  $15 \log _ { 6 } x ( x - 6 )$ 
D)  $\log _ { 6 } x ^ { 3 } ( x - 6 ) ^ { 5 }$ 
A)  $\log _ { 6 } x ( x - 6 )$ 
B)  $\log _ { 6 } x ( x - 6 ) ^ { 15 }$ 
C)  $15 \log _ { 6 } x ( x - 6 )$ 
D)  $\log _ { 6 } x ^ { 3 } ( x - 6 ) ^ { 5 }$

Question 15

Express as a single logarithm.
-$\left( \log _ { a } x - \log _ { a } y \right) + 5 \log _ { a } z$

Accepted Answer

A)  $\log _ { a } \frac { x } { z ^ { 5 } y }$ 
B)  $\log _ { a } \frac { 5 x z } { y }$ 
C)  $\log _ { \mathrm { a } } \frac { \mathrm { xz } 5 } { \mathrm { y } }$ 
D)  $\log _ { a } x z ^ { 5 } y$ 
A)  $\log _ { a } \frac { x } { z ^ { 5 } y }$ 
B)  $\log _ { a } \frac { 5 x z } { y }$ 
C)  $\log _ { \mathrm { a } } \frac { \mathrm { xz } 5 } { \mathrm { y } }$ 
D)  $\log _ { a } x z ^ { 5 } y$

Question 16

Solve the problem.
-Find the amount in a savings account at the end of 7 years if the amount originally deposited is $3,000 and the interest rate is 5.5% compounded quarterly. Use: $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$ where:
$\mathrm { A } =$ final amount
$\mathrm { P } = \$ 3,000$ (the initial deposit)
$r = 5.5 \% = 0.055$ (the annual rate of interest)
$\mathrm { n } = 4$ (the number of times interest is compounded each year)
$t = 7$ (the duration of the deposit in years)

Accepted Answer

A)  $\$ 85,155.00$ 
B)  $\$ 4,397.29$ 
C)  $\$ 3,300.94$ 
D)  $\$ 4,837.02$ 
A)  $\$ 85,155.00$ 
B)  $\$ 4,397.29$ 
C)  $\$ 3,300.94$ 
D)  $\$ 4,837.02$

Question 17

Determine whether the given function is exponential or not. If it is exponential, identify the value of the base a.
-$\begin{array}{cl}
\hline \mathrm{x} & \mathrm{H}(\mathrm{x}) \
\hline-1 & \frac{5}{8} \
0 & 1 \
1 & \frac{8}{5} \\
2 & \frac{64}{25} \\
3 & \frac{512}{125} \\
\hline
\end{array}$

Accepted Answer

A)  Exponential; $a = \frac { 5 } { 8 }$ 
B)  Exponential; $a = 8$ 
C)  Exponential; $a = \frac { 8 } { 5 }$ 
D)  Not exponential 
A)  Exponential; $a = \frac { 5 } { 8 }$ 
B)  Exponential; $a = 8$ 
C)  Exponential; $a = \frac { 8 } { 5 }$ 
D)  Not exponential

Question 18

Find the domain of the function.
-$$f ( x ) = 2 - \ln ( 3 x )$$

Accepted Answer

A)  $( 3 , \infty )$ 
B)  $( - 2,3 )$ 
C)  $( 0 , \infty )$ 
D)  $( - \infty , 2 ) \cup ( 3 , \infty )$ 
A)  $( 3 , \infty )$ 
B)  $( - 2,3 )$ 
C)  $( 0 , \infty )$ 
D)  $( - \infty , 2 ) \cup ( 3 , \infty )$

Question 19

Write as the sum and/or difference of logarithms. Express powers as factors.
-$$\log _ { 7 } \frac { 5 } { 9 }$$

Accepted Answer

A)  $\log _ { 7 } 9 - \log _ { 7 } 5$ 
B)  $\log _ { 7 } 5 + \log _ { 7 } 5$ 
C)  $\log _ { 7 } 5 \div \log _ { 7 } 9$ 
D)  $\log _ { 7 } 5 - \log _ { 7 } 9$ 
A)  $\log _ { 7 } 9 - \log _ { 7 } 5$ 
B)  $\log _ { 7 } 5 + \log _ { 7 } 5$ 
C)  $\log _ { 7 } 5 \div \log _ { 7 } 9$ 
D)  $\log _ { 7 } 5 - \log _ { 7 } 9$

Question 20

Solve the problem.
-The function f $f ( x ) = 300 ( 0.5 ) ^ { x / 90 }$ models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. Find the amount of
Radioactive material in the vault after 200 years. Round to the nearest whole number.

Accepted Answer

A)  333 pounds 
B)  220 pounds 
C)  68 pounds 
D)  64 pounds 
A)  333 pounds 
B)  220 pounds 
C)  68 pounds 
D)  64 pounds

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

Solve the equation. - $\left( \frac { 1 } { 2 } \right) ^ { x } = 8$

Graph the function. - $f(x)=-1-\ln x$ $Graph the function. - f(x)=-1-\ln x A) B) C) D)$ A) $Graph the function. - f(x)=-1-\ln x A) B) C) D)$ B) $Graph the function. - f(x)=-1-\ln x A) B) C) D)$ C) $Graph the function. - f(x)=-1-\ln x A) B) C) D)$ D) $Graph the function. - f(x)=-1-\ln x A) B) C) D)$

Decide whether or not the functions are inverses of each other. - $f ( x ) = \sqrt { x + 7 } \text {, domain } [ - 7 , \infty ) ; g ( x ) = x ^ { 2 } + 7 , \text { domain } ( - \infty , \infty )$

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. - $\log _ { ( 2 / 3 ) } 19$

Decide whether or not the functions are inverses of each other. - $f ( x ) = 4 x + 16 , g ( x ) = \frac { 1 } { 4 } x - 4$

Find the exact value of the logarithmic expression. - $\ln \mathrm { e } ^ { 8 }$

Find the domain of the function. - $f ( x ) = \ln ( - 4 - x )$

Find the domain of the composite function f $f ^ { \circ } g$ - $f ( x ) = \sqrt { x - 1 } ; \quad g ( x ) = \frac { 1 } { x - 8 }$

Express as a single logarithm. - $3 \log _ { 6 } x + 5 \log _ { 6 } ( x - 6 )$

Express as a single logarithm. - $\left( \log _ { a } x - \log _ { a } y \right) + 5 \log _ { a } z$

Determine whether the given function is exponential or not. If it is exponential, identify the value of the base a. - () -1 0 1 1 2 3

Find the domain of the function. - $f ( x ) = 2 - \ln ( 3 x )$

Write as the sum and/or difference of logarithms. Express powers as factors. - $\log _ { 7 } \frac { 5 } { 9 }$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Review

Filters

Exam 4: Exponential and Logarithmic Functions

Solve the equation. - 3⋅52t−1=753 \cdot 5 ^ { 2 t - 1 } = 753⋅52t−1=75

Solve the equation. - (12)x=8\left( \frac { 1 } { 2 } \right) ^ { x } = 8(21​)x=8

Graph the function. - f(x)=−1−ln⁡xf(x)=-1-\ln xf(x)=−1−lnx A) B) C) D)

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. - log⁡(2/3)19\log _ { ( 2 / 3 ) } 19log(2/3)​19

Decide whether or not the functions are inverses of each other. - f(x)=4x+16,g(x)=14x−4f ( x ) = 4 x + 16 , g ( x ) = \frac { 1 } { 4 } x - 4f(x)=4x+16,g(x)=41​x−4

Find the exact value of the logarithmic expression. - ln⁡e8\ln \mathrm { e } ^ { 8 }lne8

Find the domain of the function. - f(x)=ln⁡(−4−x)f ( x ) = \ln ( - 4 - x )f(x)=ln(−4−x)

Find the domain of the composite function f f∘gf ^ { \circ } g f∘g - f(x)=x−1;g(x)=1x−8f ( x ) = \sqrt { x - 1 } ; \quad g ( x ) = \frac { 1 } { x - 8 }f(x)=x−1​;g(x)=x−81​

Express as a single logarithm. - 3log⁡6x+5log⁡6(x−6)3 \log _ { 6 } x + 5 \log _ { 6 } ( x - 6 )3log6​x+5log6​(x−6)

Express as a single logarithm. - (log⁡ax−log⁡ay)+5log⁡az\left( \log _ { a } x - \log _ { a } y \right) + 5 \log _ { a } z(loga​x−loga​y)+5loga​z