Question 1

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator.
-$$\log _ { 4 } 40 - \log _ { 4 } 10$$

Accepted Answer

A)  4 
B)  10 
C)  40 
D)  1 
A)  4 
B)  10 
C)  40 
D)  1 D

Question 2

Choose the one alternative that best completes the statement or answers the question.
-The logistic growth model $\mathrm { P } ( \mathrm { t } ) = \frac { 290 } { 1 + 35.25 \mathrm { e } ^ { - 0.188 \mathrm { t } } }$ represents the population of a species introduced into a new territory after t years. What will the population be in 30 years?

Accepted Answer

A)  290 
B)  263 
C)  258 
D)  2,316 
A)  290 
B)  263 
C)  258 
D)  2,316 C

Question 3

Write the word or phrase that best completes each statement or answers the question.
-$$16 ^ { 3 / 2 } = 64$$

Accepted Answer

$$\log _ { 16 } 64 = \frac { 3 } { 2 }$$

Question 4

For the given functions f and g, find the requested composite function.
-$f ( x ) = 4 x ^ { 2 } + 6 x + 3 , \quad g ( x ) = 6 x - 7 ; \quad$ Find $( g \circ f ) ( x )$

Accepted Answer

A)  $4 x ^ { 2 } + 36 x + 11$ 
B)  $24 x ^ { 2 } + 36 x + 25$ 
C)  $4 x ^ { 2 } + 6 x - 4$ 
D)  $24 x ^ { 2 } + 36 x + 11$ 
A)  $4 x ^ { 2 } + 36 x + 11$ 
B)  $24 x ^ { 2 } + 36 x + 25$ 
C)  $4 x ^ { 2 } + 6 x - 4$ 
D)  $24 x ^ { 2 } + 36 x + 11$

Question 5

Choose the one alternative that best completes the statement or answers the question.
-The population of a particular country was 30 million in 1984; in 1995, it was 34 million. The exponential growth function describes the population of this country t years after 1984. Use the fact that 11 years $$\mathrm { A } = 30 \mathrm { e } ^ { \mathrm { kt } }$$ after 1984 the population increased by 4 million to find k to three decimal places.

Accepted Answer

A)  0.126 
B)  0.011 
C)  0.630 
D)  0.021 
A)  0.126 
B)  0.011 
C)  0.630 
D)  0.021

Question 6

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

Question 7

Solve the problem.
-$$\text { Find the value of } \log _ { 3 } 4 \cdot \log _ { 4 } 5 \cdot \log _ { 5 } 6 \cdot \log _ { 6 } 7 \cdot \log _ { 7 } 8 \cdot \log _ { 8 } 9$$

Accepted Answer

The answer of Solve the problem.
-\[\text { Find the value...

Question 8

Change the logarithmic expression to an equivalent expression involving an exponent.
-$\log _ { b } 81 = 4$

Accepted Answer

A)  $81 ^ { b } = 4$ 
B)  $81 ^ { 4 } = b$ 
C)  $b ^ { 4 } = 81$ 
D)  $4 ^ { b } = 81$ 
A)  $81 ^ { b } = 4$ 
B)  $81 ^ { 4 } = b$ 
C)  $b ^ { 4 } = 81$ 
D)  $4 ^ { b } = 81$

Question 9

Choose the one alternative that best completes the statement or answers the question.
-A thermometer reading $11 ^ { \circ } \mathrm { C }$ is brought into a room with a constant temperature of $30 ^ { \circ } \mathrm { C }$. If the thermometer reads $17 ^ { \circ } \mathrm { C }$ after 4 minutes, what will it read after being in the room for 7 minutes? Assume the cooling follows Newton's Law of Cooling:
$$\mathrm { U } = \mathrm { T } + \left( \mathrm { U } _ { \mathrm { O } } - \mathrm { T } \right) \mathrm { e } ^ { \mathrm { kt } } \text {. }$$
(Round your answer to two decimal places.)

Accepted Answer

A)  $28.67 ^ { \circ } \mathrm { C }$ 
B)  $5.87 ^ { \circ } \mathrm { C }$ 
C)  $20.22 ^ { \circ } \mathrm { C }$ 
D)  $39.78 ^ { \circ } \mathrm { C }$ 
A)  $28.67 ^ { \circ } \mathrm { C }$ 
B)  $5.87 ^ { \circ } \mathrm { C }$ 
C)  $20.22 ^ { \circ } \mathrm { C }$ 
D)  $39.78 ^ { \circ } \mathrm { C }$

Question 10

Solve the equation.
-$$2 ( 7 - 3 x ) = \frac { 1 } { 4 }$$

Accepted Answer

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

Question 11

Approximate the value using a calculator. Express answer rounded to three decimal places.
-$3.2 ^ { 2.84 }$

Accepted Answer

A)  $9.088$ 
B)  $27.204$ 
C)  $28.224$ 
D)  $41.350$ 
A)  $9.088$ 
B)  $27.204$ 
C)  $28.224$ 
D)  $41.350$

Question 12

Write the word or phrase that best completes each statement or answers the question.
-$$\log _ { b } \sqrt [ 3 ] { \frac { x ^ { 5 } y ^ { 8 } } { z ^ { 2 } } }$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 13

Choose the one alternative that best completes the statement or answers the question.
-The logistic growth function $f ( t ) = \frac { 440 } { 1 + 6.3 e ^ { - 0.2 t } }$ describes the population of a species of butterflies t months after they are introduced to a non-threatening habitat. What is the limiting size of the butterfly population that the habitat will sustain?

Accepted Answer

A)  60 butterflies 
B)  440 butterflies 
C)  6 butterflies 
D)  880 butterflies 
A)  60 butterflies 
B)  440 butterflies 
C)  6 butterflies 
D)  880 butterflies

Question 14

Find the exact value of the logarithmic expression.
-$\log _ { 8 } 1$

Accepted Answer

A)  $\frac { 1 } { 8 }$ 
B)  0 
C)  1 
D)  8 
A)  $\frac { 1 } { 8 }$ 
B)  0 
C)  1 
D)  8

Question 15

Decide whether or not the functions are inverses of each other.
-$$f ( x ) = 8 x - 9 , g ( x ) = \frac { x + 8 } { 9 }$$

Accepted Answer

A)  $\mathrm { No }$ 
B)  Yes 
A)  $\mathrm { No }$ 
B)  Yes

Question 16

Solve the equation.
-$$4 ^ { x } = 256$$

Accepted Answer

A)  $\{ 3 \}$ 
B)  $\{ 5 \}$ 
C)  $\{ 64 \}$ 
D)  $\{ 4 \}$ 
A)  $\{ 3 \}$ 
B)  $\{ 5 \}$ 
C)  $\{ 64 \}$ 
D)  $\{ 4 \}$

Question 17

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator.
-$$\log _ { 4 } 24 - \log _ { 4 } 6$$

Accepted Answer

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

Question 18

Choose the one alternative that best completes the statement or answers the question.
-Money magazine reports that the percentage of trading days in which the Dasdaq loses or gains $2 \%$ or more has been increasing since 1995 indicating more volatility in the Dasdaq. Use a graphing utility to fit an exponential function to the data. Predict the percentage of trading days in 2001 having such swings in value.
$\begin{array}{l|l}
\text { Year } & \% \text { of trading days } \
\hline 1995,0 & 2 \
1996,1 & 5 \
1997,2 & 8 \
1998,3 & 18 \
1999,4 & 23 \
2000,5 & 49
\end{array}$

Accepted Answer

A)  $y = 2.353 \mathrm { e } ^ { 0.610 x , 91 \text { days } }$ 
B)  $\mathrm { y } = 1.669 \mathrm { x } ^ { 1.706,46 \text { days } }$ 
C)  $\mathrm { y } = 1.278 \mathrm { e } ^ { 0.611 \mathrm { x } , 92 \mathrm { days } }$ 
D)  $\mathrm { y } = 1.849 \mathrm { e } ^ { 0.531 \mathrm { x } , 76 \mathrm { days } }$ 
A)  $y = 2.353 \mathrm { e } ^ { 0.610 x , 91 \text { days } }$ 
B)  $\mathrm { y } = 1.669 \mathrm { x } ^ { 1.706,46 \text { days } }$ 
C)  $\mathrm { y } = 1.278 \mathrm { e } ^ { 0.611 \mathrm { x } , 92 \mathrm { days } }$ 
D)  $\mathrm { y } = 1.849 \mathrm { e } ^ { 0.531 \mathrm { x } , 76 \mathrm { days } }$

Question 19

Change the exponential expression to an equivalent expression involving a logarithm.
-$$3 ^ { - 2 } = \frac { 1 } { 9 }$$

Accepted Answer

A)  $\log _ { - 2 } \frac { 1 } { 9 } = 3$ 
B)  $\log _ { 1 / 9 } 3 = - 2$ 
C)  $\log _ { 3 } \frac { 1 } { 9 } = - 2$ 
D)  $\log _ { 3 } - 2 = \frac { 1 } { 9 }$ 
A)  $\log _ { - 2 } \frac { 1 } { 9 } = 3$ 
B)  $\log _ { 1 / 9 } 3 = - 2$ 
C)  $\log _ { 3 } \frac { 1 } { 9 } = - 2$ 
D)  $\log _ { 3 } - 2 = \frac { 1 } { 9 }$

Question 20

Choose the one alternative that best completes the statement or answers the question.
-$\mathrm { pH } = - \log _ { 10 } \left[ \mathrm { H } ^ { + } \right]$Find the $\left[ \mathrm { H } ^ { + } \right]$if the $\mathrm { pH } = 1.4$.

Accepted Answer

A)  $2.51 \times 10 ^ { - 1 }$ 
B)  $3.98 \times 10 ^ { - 1 }$ 
C)  $3.98 \times 10 ^ { - 2 }$ 
D)  $2.51 \times 10 ^ { - 2 }$ 
A)  $2.51 \times 10 ^ { - 1 }$ 
B)  $3.98 \times 10 ^ { - 1 }$ 
C)  $3.98 \times 10 ^ { - 2 }$ 
D)  $2.51 \times 10 ^ { - 2 }$

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - $\log _ { 4 } 40 - \log _ { 4 } 10$

Write the word or phrase that best completes each statement or answers the question. - $16 ^ { 3 / 2 } = 64$

For the given functions f and g, find the requested composite function. - $f ( x ) = 4 x ^ { 2 } + 6 x + 3 , \quad g ( x ) = 6 x - 7 ; \quad$ Find $( g \circ f ) ( x )$

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

Solve the problem. - $\text { Find the value of } \log _ { 3 } 4 \cdot \log _ { 4 } 5 \cdot \log _ { 5 } 6 \cdot \log _ { 6 } 7 \cdot \log _ { 7 } 8 \cdot \log _ { 8 } 9$

Change the logarithmic expression to an equivalent expression involving an exponent. - $\log _ { b } 81 = 4$

Solve the equation. - $2 ( 7 - 3 x ) = \frac { 1 } { 4 }$

Approximate the value using a calculator. Express answer rounded to three decimal places. - $3.2 ^ { 2.84 }$

Write the word or phrase that best completes each statement or answers the question. - $\log _ { b } \sqrt [ 3 ] { \frac { x ^ { 5 } y ^ { 8 } } { z ^ { 2 } } }$

Find the exact value of the logarithmic expression. - $\log _ { 8 } 1$

Decide whether or not the functions are inverses of each other. - $f ( x ) = 8 x - 9 , g ( x ) = \frac { x + 8 } { 9 }$

Solve the equation. - $4 ^ { x } = 256$

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - $\log _ { 4 } 24 - \log _ { 4 } 6$

Change the exponential expression to an equivalent expression involving a logarithm. - $3 ^ { - 2 } = \frac { 1 } { 9 }$

Choose the one alternative that best completes the statement or answers the question. - $\mathrm { pH } = - \log _ { 10 } \left[ \mathrm { H } ^ { + } \right]$ Find the $\left[ \mathrm { H } ^ { + } \right]$ if the $\mathrm { pH } = 1.4$ .

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

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 4: Exponential and Logarithmic Functions

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - log⁡440−log⁡410\log _ { 4 } 40 - \log _ { 4 } 10log4​40−log4​10

Write the word or phrase that best completes each statement or answers the question. - 163/2=6416 ^ { 3 / 2 } = 64163/2=64

For the given functions f and g, find the requested composite function. - f(x)=4x2+6x+3,g(x)=6x−7;f ( x ) = 4 x ^ { 2 } + 6 x + 3 , \quad g ( x ) = 6 x - 7 ; \quadf(x)=4x2+6x+3,g(x)=6x−7; Find (g∘f)(x)( g \circ f ) ( x )(g∘f)(x)

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

Change the logarithmic expression to an equivalent expression involving an exponent. - log⁡b81=4\log _ { b } 81 = 4logb​81=4

Solve the equation. - 2(7−3x)=142 ( 7 - 3 x ) = \frac { 1 } { 4 }2(7−3x)=41​

Approximate the value using a calculator. Express answer rounded to three decimal places. - 3.22.843.2 ^ { 2.84 }3.22.84

Write the word or phrase that best completes each statement or answers the question. - log⁡bx5y8z23\log _ { b } \sqrt [ 3 ] { \frac { x ^ { 5 } y ^ { 8 } } { z ^ { 2 } } }logb​3z2x5y8​​

Find the exact value of the logarithmic expression. - log⁡81\log _ { 8 } 1log8​1

Decide whether or not the functions are inverses of each other. - f(x)=8x−9,g(x)=x+89f ( x ) = 8 x - 9 , g ( x ) = \frac { x + 8 } { 9 }f(x)=8x−9,g(x)=9x+8​

Solve the equation. - 4x=2564 ^ { x } = 2564x=256

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - log⁡424−log⁡46\log _ { 4 } 24 - \log _ { 4 } 6log4​24−log4​6

Change the exponential expression to an equivalent expression involving a logarithm. - 3−2=193 ^ { - 2 } = \frac { 1 } { 9 }3−2=91​

Choose the one alternative that best completes the statement or answers the question. - pH=−log⁡10[H+]\mathrm { pH } = - \log _ { 10 } \left[ \mathrm { H } ^ { + } \right]pH=−log10​[H+] Find the [H+]\left[ \mathrm { H } ^ { + } \right][H+] if the pH=1.4\mathrm { pH } = 1.4pH=1.4 .