Question 1

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

Accepted Answer

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

Question 2

Use a calculator to find the natural logarithm correct to four decimal places.
-In $0.000356$

Accepted Answer

A)  $- 7.9406$ 
B)  $3.4486$ 
C)  $- 3.4486$ 
D)  $7.9406$ 
A)  $- 7.9406$ 
B)  $3.4486$ 
C)  $- 3.4486$ 
D)  $7.9406$

Question 3

The function f is one-to-one. Find its inverse.
-$$f ( x ) = ( x + 7 ) ^ { 3 }$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } + 7$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } } - 343$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } } - 7$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } } - 7$ 
A)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } + 7$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } } - 343$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } } - 7$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } } - 7$

Question 4

Solve the problem.
-A culture of bacteria obeys the law of uninhibited growth. If 140,000 bacteria are present initially and there are
609,000 after 6 hours, how long will it take for the population to reach one million?

Accepted Answer

The answer of Solve the problem.
-A culture of bacteria obeys...

Question 5

Solve the problem.
-A grocery store normally sells 8 jars of caviar per week. Use the Poisson Distribution $P ( x ) = \frac { 8 ^ { x } e ^ { - 8 } } { x ! }$ to find the probability (to three decimals) of selling 3 jars in a week. $( x ! = x \cdot ( x - 1 ) \cdot ( x - 2 ) \cdot \ldots \cdot ( 3 ) ( 2 ) ( 1 ) )$

Accepted Answer

A)  0.057 
B)  0.019 
C)  0.086 
D)  0.029 
A)  0.057 
B)  0.019 
C)  0.086 
D)  0.029

Question 6

Solve the problem.
-$$\text { If } f ( x ) = \frac { 1 } { 2 } x ^ { 2 } + 4 \text { and } g ( x ) = 2 x - a \text {, find a so that the graph of } f \circ g \text { crosses the } y \text {-axis at } 36$$

Accepted Answer

The answer of Solve the problem.
-\[\text { If } f...

Question 7

Change the exponential expression to an equivalent expression involving a logarithm.
-$$x ^ { \sqrt { 5 } } = \pi$$

Accepted Answer

A)  $x = \log _ { \pi } \sqrt { 5 }$ 
B)  $x = \log _ { \sqrt { 5 } } \pi$ 
C)  $\sqrt { 5 } = \log _ { \pi } x$ 
D)  $\sqrt { 5 } = \log _ { \mathrm { x } } \pi$ 
A)  $x = \log _ { \pi } \sqrt { 5 }$ 
B)  $x = \log _ { \sqrt { 5 } } \pi$ 
C)  $\sqrt { 5 } = \log _ { \pi } x$ 
D)  $\sqrt { 5 } = \log _ { \mathrm { x } } \pi$

Question 8

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator.
-$\log _ { 30 } 10 + \log _ { 30 } 3$

Accepted Answer

A)  10 
B)  1 
C)  30 
D)  3 
A)  10 
B)  1 
C)  30 
D)  3

Question 9

Find functions f and g so that f $f \circ g = H$
-$$H ( x ) = | 9 x + 3 |$$

Accepted Answer

A)  $f ( x ) = | - x | ; \quad g ( x ) = 9 x - 3$ 
B)  $f ( x ) = - | x |$; $g ( x ) = 9 x + 3$ 
C)  $f ( x ) = x ; g ( x ) = 9 x + 3$ 
D)  $f ( x ) = | x | ; \quad g ( x ) = 9 x + 3$ 
A)  $f ( x ) = | - x | ; \quad g ( x ) = 9 x - 3$ 
B)  $f ( x ) = - | x |$; $g ( x ) = 9 x + 3$ 
C)  $f ( x ) = x ; g ( x ) = 9 x + 3$ 
D)  $f ( x ) = | x | ; \quad g ( x ) = 9 x + 3$

Question 10

Solve the equation.
-$\log _ { 8 } x ^ { 2 } = 4$

Accepted Answer

A)  $\{ 4 \sqrt { 2 } , - 4 \sqrt { 2 } \}$ 
B)  $\{ 4,096 \}$ 
C)  $\{ 256 \}$ 
D)  $\{ 64 , - 64 \}$ 
A)  $\{ 4 \sqrt { 2 } , - 4 \sqrt { 2 } \}$ 
B)  $\{ 4,096 \}$ 
C)  $\{ 256 \}$ 
D)  $\{ 64 , - 64 \}$

Question 11

Solve the problem.
-In a Psychology class, the students were tested at the end of the course on a final exam. Then they were retested with an equivalent test at subsequent time intervals. Their average scores after t months are given in the table. $$\begin{array} { l | c c c c c } 
\text { Time, t ( in months) } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Score, y ( in percentage) } & 86.2 & 85.7 & 85.4 & 85.2 & 85.0
\end{array}$$ Using a graphing utility, fit a logarithmic function y $$y = a + b \ln x$$ the data. Using the function you found, estimate
How long will it take for the test scores to fall below 84%. Express your answer to the nearest month.

Accepted Answer

A)  8 months 
B)  12 months 
C)  20 months 
D)  10 months 
A)  8 months 
B)  12 months 
C)  20 months 
D)  10 months

Question 12

Change the logarithmic expression to an equivalent expression involving an exponent.
-$$\log _ { \pi } 37 = x$$

Accepted Answer

A)  $\pi ^ { x } = \frac { 1 } { 37 }$ 
B)  $x ^ { \pi } = 37$ 
C)  $37 ^ { x } = \pi$ 
D)  $\pi ^ { x } = 37$ 
A)  $\pi ^ { x } = \frac { 1 } { 37 }$ 
B)  $x ^ { \pi } = 37$ 
C)  $37 ^ { x } = \pi$ 
D)  $\pi ^ { x } = 37$

Question 13

Solve the equation.
-$\log _ { x } \left( \frac { 2 } { 5 } \right) = 1$

Accepted Answer

A)  $\left\{ \frac { 2 } { 5 } \right\}$ 
B)  2 
C)  $\left\{ \frac { 5 } { 2 } \right\}$ 
D)  1 
A)  $\left\{ \frac { 2 } { 5 } \right\}$ 
B)  2 
C)  $\left\{ \frac { 5 } { 2 } \right\}$ 
D)  1

Question 14

Find the effective rate of interest.
-25.12% compounded daily

Accepted Answer

A)  25.243% 
B)  25.325% 
C)  26.025% 
D)  28.546% 
A)  25.243% 
B)  25.325% 
C)  26.025% 
D)  28.546%

Question 15

Solve the problem.
-The concentration of alcohol in a person's blood is measurable. Suppose that the risk R (given as a percent) of having an
accident while driving a car can be modeled by the equation $R = 5 e ^ { k x }$ where x is the variable concentration of alcohol in the blood and k is a constant.
Suppose that a concentration of alcohol in the blood of 0.07 results in a 10% risk (R = 10) of an accident. Find the
constant k in the equation.
Using this value of k, what is the risk if the concentration is 0.11?

Accepted Answer

The answer of Solve the problem.
-The concentration of alcohol in...

Question 16

Write the word or phrase that best completes each statement or answers the question.
-$$\pi ^ { x + 1 } = e ^ { 2 x }$$

Accepted Answer

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

Question 17

Solve the problem.
-The concentration of alcohol in a person's blood is measurable. Suppose that the risk R (given as a percent) of having an
accident while driving a car can be modeled by the equation $$\mathrm { R } = 4 \mathrm { e } ^ { \mathrm { kx } }$$ where x is the variable concentration of alcohol in the blood and k is a constant.
(a) Suppose that a concentration of alcohol in the blood of 0.09 results in a 14% risk (R = 14) of an accident. Find the
constant k in the equation.
(b) Using this value of k, what is the risk if the concentration is 0.014?
(c) Using the same value of k, what concentration of alcohol corresponds to a risk of 100%?
(d) If the law asserts that anyone with a risk of having an accident of 12 or more should not have driving privileges,
at what concentration of alcohol in the blood should a driver be arrested and charged with a DUI?

Accepted Answer

(a) k = 13

Question 18

Solve the equation.
-$$\left( \frac { 1 } { 3 } \right) ^ { 4 x + 5 } = 9 ^ { x - 2 }$$

Accepted Answer

A)  $\left\{ - \frac { 1 } { 6 } \right\}$ 
B)  $\left\{ \frac { 9 } { 4 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 2 } \right\}$ 
D)  $\left\{ - \frac { 3 } { 5 } \right\}$ 
A)  $\left\{ - \frac { 1 } { 6 } \right\}$ 
B)  $\left\{ \frac { 9 } { 4 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 2 } \right\}$ 
D)  $\left\{ - \frac { 3 } { 5 } \right\}$

Question 19

Change the logarithmic expression to an equivalent expression involving an exponent.
-$\log _ { 1 / 3 } 9 = - 2$

Accepted Answer

A)  $\left( \frac { 1 } { 3 } \right) ^ { 2 } = 9$ 
B)  $\left( \frac { 1 } { 3 } \right) ^ { - 2 } = 9$ 
C)  $( - 2 ) ^ { 1 / 3 } = 9$ 
D)  $9 ^ { 1 / 3 } = 2$ 
A)  $\left( \frac { 1 } { 3 } \right) ^ { 2 } = 9$ 
B)  $\left( \frac { 1 } { 3 } \right) ^ { - 2 } = 9$ 
C)  $( - 2 ) ^ { 1 / 3 } = 9$ 
D)  $9 ^ { 1 / 3 } = 2$

Question 20

The function f is one-to-one. Find its inverse.
-$$f ( x ) = \frac { 6 } { x }$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { x } { 6 }$ 
B)  $f ^ { - 1 } ( x ) = - 6 x$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 6 } { \mathrm { x } }$ 
D)  $f ^ { - 1 } ( x ) = 6 x$ 
A)  $f ^ { - 1 } ( x ) = \frac { x } { 6 }$ 
B)  $f ^ { - 1 } ( x ) = - 6 x$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 6 } { \mathrm { x } }$ 
D)  $f ^ { - 1 } ( x ) = 6 x$

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

Use a calculator to find the natural logarithm correct to four decimal places. -In $0.000356$

The function f is one-to-one. Find its inverse. - $f ( x ) = ( x + 7 ) ^ { 3 }$

Solve the problem. -A culture of bacteria obeys the law of uninhibited growth. If 140,000 bacteria are present initially and there are 609,000 after 6 hours, how long will it take for the population to reach one million?

Solve the problem. - $\text { If } f ( x ) = \frac { 1 } { 2 } x ^ { 2 } + 4 \text { and } g ( x ) = 2 x - a \text {, find a so that the graph of } f \circ g \text { crosses the } y \text {-axis at } 36$

Change the exponential expression to an equivalent expression involving a logarithm. - $x ^ { \sqrt { 5 } } = \pi$

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - $\log _ { 30 } 10 + \log _ { 30 } 3$

Find functions f and g so that f $f \circ g = H$ - $H ( x ) = | 9 x + 3 |$

Solve the equation. - $\log _ { 8 } x ^ { 2 } = 4$

Change the logarithmic expression to an equivalent expression involving an exponent. - $\log _ { \pi } 37 = x$

Solve the equation. - $\log _ { x } \left( \frac { 2 } { 5 } \right) = 1$

Find the effective rate of interest. -25.12% compounded daily

Write the word or phrase that best completes each statement or answers the question. - $\pi ^ { x + 1 } = e ^ { 2 x }$

Solve the equation. - $\left( \frac { 1 } { 3 } \right) ^ { 4 x + 5 } = 9 ^ { x - 2 }$

Change the logarithmic expression to an equivalent expression involving an exponent. - $\log _ { 1 / 3 } 9 = - 2$

The function f is one-to-one. Find its inverse. - $f ( x ) = \frac { 6 } { x }$

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

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Exam 4: Exponential and Logarithmic Functions

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

Use a calculator to find the natural logarithm correct to four decimal places. -In 0.0003560.0003560.000356

The function f is one-to-one. Find its inverse. - f(x)=(x+7)3f ( x ) = ( x + 7 ) ^ { 3 }f(x)=(x+7)3