Question 1

Evaluate the logarithm.
-$\log _ { 5 } 5$

Accepted Answer

A)  0 
B)  10 
C)  5 
D)  1 
A)  0 
B)  10 
C)  5 
D)  1

Question 2

Solve the problem.
-A certain noise has an intensity I of $9.54 \times 10 ^ { - 5 }$. Given that decibel level D is related to intensity by $\mathrm { D } = 10 \log \left( \frac { \mathrm { I } } { \mathrm { I } _ { 0 } } \right)$, where $\mathrm { I } _ { 0 }$ is $10 ^ { - 12 }$, determine the decibel level of the noise. Round your answer to the nearest decibel.

Accepted Answer

A)  80 decibels 
B)  184 decibels 
C)  70 decibels 
D)  8 decibels 
A)  80 decibels 
B)  184 decibels 
C)  70 decibels 
D)  8 decibels

Question 3

Choose the one alternative that best completes the statement or answers the question.
-The height in meters of women of a certain tribe is approximated by $\mathrm { h } = 0.52 + 2 \log ( \mathrm { t } / 3 )$ where $\mathrm { t }$ is the woman's age in years and $1 \leq t \leq 20$. Estimate the height (to the nearest hundredth) of a woman of the tribe 4 years of age. (Round to the nearest hundredth.)

Accepted Answer

A)  $1.12 \mathrm {~m}$ 
B)  $0.96 \mathrm {~m}$ 
C)  $0.52 \mathrm {~m}$ 
D)  $0.77 \mathrm {~m}$ 
A)  $1.12 \mathrm {~m}$ 
B)  $0.96 \mathrm {~m}$ 
C)  $0.52 \mathrm {~m}$ 
D)  $0.77 \mathrm {~m}$

Question 4

Choose the one alternative that best completes the statement or answers the question.
-A certain radioactive isotope decays at a rate of $0.2 \%$ annually. Determine the half-life of this isotope, to the nearest year.

Accepted Answer

A)  $151 \mathrm { yr }$ 
B)  $347 \mathrm { yr }$ 
C)  $3 \mathrm { yr }$ 
D)  $250 \mathrm { yr }$ 
A)  $151 \mathrm { yr }$ 
B)  $347 \mathrm { yr }$ 
C)  $3 \mathrm { yr }$ 
D)  $250 \mathrm { yr }$

Question 5

Use properties of logarithms to evaluate the expression.
-If $f ( x ) = e ^ { x }$, find $f \left[ \ln \left( \frac { 1 } { e ^ { 2 } } \right) \right]$

Accepted Answer

A)  $\ln \mathrm { e }$ 
B)  $e ^ { 1 / x }$ 
C)  $\frac { 1 } { \mathrm { e } ^ { 2 } }$ 
D)  $- 2$ 
A)  $\ln \mathrm { e }$ 
B)  $e ^ { 1 / x }$ 
C)  $\frac { 1 } { \mathrm { e } ^ { 2 } }$ 
D)  $- 2$

Question 6

Graph the exponential function using transformations where appropriate.
-$$f ( x ) = - 4 ^ { x - 1 }$$

Accepted Answer

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

Question 7

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or
reflected.
-

Accepted Answer

A)  $\log _ { 2 } ( - x + 3 ) + 1$ 
B)  $\log _ { 2 } ( x - 3 ) - 1$ 
C)  $\log _ { 2 } ( - x + 3 ) - 1$ 
D)  $\log _ { 2 } ( x - 3 ) + 1$ 
A)  $\log _ { 2 } ( - x + 3 ) + 1$ 
B)  $\log _ { 2 } ( x - 3 ) - 1$ 
C)  $\log _ { 2 } ( - x + 3 ) - 1$ 
D)  $\log _ { 2 } ( x - 3 ) + 1$

Question 8

Evaluate the logarithm.
-$\log _ { 8 } 512$

Accepted Answer

A)  512 
B)  8 
C)  24 
D)  3 
A)  512 
B)  8 
C)  24 
D)  3

Question 9

Use the alphabet coding method (A =1, B = 2, C = 3, ... Z = 26) to
-The function defined by $f ( x ) = 3 x - 4$ was used to encode a message as:
$$\begin{array} { l l l l l l l l l l } 
38 & 11 & 62 & 11 & 50 & - 1 & 17 & - 1 & 23 & 38
\end{array}$$
Find the inverse function and determine the message.

Accepted Answer

The answer of Use the alphabet coding method (A =1,...

Question 10

Choose the one alternative that best completes the statement or answers the question.
-Use the formu $\mathrm { P } = \mathrm { Ie }^{ \mathrm { kt }}$ . A bacterial culture has an initial population of 10,000. If its population 441) declines to 6000 in 4 hours, what will it be at the end of 6 hours?

Accepted Answer

A)  2000 
B)  2324 
C)  4648 
D)  7114 
A)  2000 
B)  2324 
C)  4648 
D)  7114

Question 11

Choose the one alternative that best completes the statement or answers the question.
-Coffee is best enjoyed at a temperature of 124°F. A restaurant owner wants to discover the 459) temperature T at which he should serve his coffee so that it will have cooled to this ideal
Temperature in 3 minutes. He discovers that a cup of coffee served at 198°F cools to 183°F in one
Minute when his restaurant is at 74°F. If he maintains the restaurant temperature at 74°F, at what
Temperature should he serve the coffee to meet his goal?

Accepted Answer

A)  148°F 
B)  198°F 
C)  143°F 
D)  168°F 
A)  148°F 
B)  198°F 
C)  143°F 
D)  168°F

Question 12

Write in logarithmic form.
-$$10 ^ { - 5 } = 0.00001$$

Accepted Answer

A)  $\log _ { 5 } - 5 = 0.10$ 
B)  $\log _ { 5 } 0.10 = - 5$ 
C)  $\log _ { 10 } - 5 = 0.00001$ 
D)  $\log _ { 10 } 0.00001 = - 5$ 
A)  $\log _ { 5 } - 5 = 0.10$ 
B)  $\log _ { 5 } 0.10 = - 5$ 
C)  $\log _ { 10 } - 5 = 0.00001$ 
D)  $\log _ { 10 } 0.00001 = - 5$

Question 13

Use a graphing calculator to graph the function using the given viewing window. Use the graph to decide if the function
is one-to-one. If the function is one-to-one, give the equation of the inverse function.
-$f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - x + 3 ; [ - 2,4 ]$ by $[ - 20,20 ]$

Accepted Answer

A)  one-to-one; $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x - 3 } - x$ 
B)  not one-to-one 
C)  one-to-one; $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x - 3 }$ 
D)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } ^ { 2 } - 3 \mathrm { x } + 3 }$ 
A)  one-to-one; $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x - 3 } - x$ 
B)  not one-to-one 
C)  one-to-one; $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x - 3 }$ 
D)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } ^ { 2 } - 3 \mathrm { x } + 3 }$

Question 14

Graph the exponential function using transformations where appropriate.
-$f(x)=\left(\frac{1}{5}\right)^{x}+2$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
11ed7a17_f525_e0db_a20d_b7844 
A) 
  
B) 
  
C) 
  
D) 
11ed7a17_f525_e0db_a20d_b7844

Question 15

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or
reflected.
-

Accepted Answer

A)  $- \log _ { 3 } ( - x + 1 )$ 
B)  $- \log _ { 3 } ( x - 1 )$ 
C)  $- \log _ { 3 } ( x + 1 )$ 
D)  $\log _ { 3 } ( - x - 1 )$ 
A)  $- \log _ { 3 } ( - x + 1 )$ 
B)  $- \log _ { 3 } ( x - 1 )$ 
C)  $- \log _ { 3 } ( x + 1 )$ 
D)  $\log _ { 3 } ( - x - 1 )$

Question 16

Solve the equation. Give the answer in exact form.
-$$e ^ { 2 x } - 9 e ^ { x } + 20 = 0$$

Accepted Answer

A)  $\left\{ \mathrm { e } ^ { 5 } , \mathrm { e } ^ { 4 } \right\}$ 
B)  $\left\{ \frac { 5 } { \mathrm { e } } , \frac { 4 } { \mathrm { e } } \right\}$ 
C)  $\{ \ln ( - 5 ) , \ln ( - 4 ) \}$ 
D)  $\{ \ln 5 , \ln 4 \}$ 
A)  $\left\{ \mathrm { e } ^ { 5 } , \mathrm { e } ^ { 4 } \right\}$ 
B)  $\left\{ \frac { 5 } { \mathrm { e } } , \frac { 4 } { \mathrm { e } } \right\}$ 
C)  $\{ \ln ( - 5 ) , \ln ( - 4 ) \}$ 
D)  $\{ \ln 5 , \ln 4 \}$

Question 17

Decide whether the given functions are inverses.
-$\begin{array} { l } 
f = \{ ( - 3 , - 5 ) , ( 1,3 ) , ( 3 , - 3 ) , ( 7,11 ) \} \
g = \{ ( - 5 , - 3 ) , ( 3,1 ) , ( - 3,3 ) , ( 11,7 ) \}
\end{array}$

Accepted Answer

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

Question 18

Solve the following graphically. If necessary, round answers to the nearest thousandth.
-$$\mathrm { e } ^ { \mathrm { x } + \ln 3 = 2 \mathrm { e } ^ { \mathrm { x } } }$$

Accepted Answer

A)  $\{ 0.901 \}$ 
B)  $\{ 1.099 \}$ 
C)  $\{ 0.549 \}$ 
D)  $\varnothing$ 
A)  $\{ 0.901 \}$ 
B)  $\{ 1.099 \}$ 
C)  $\{ 0.549 \}$ 
D)  $\varnothing$

Question 19

Graph the function. Give the domain and range.
-$$f ( x ) = \log _ { 1 / 8 } x$$

Accepted Answer

A)  domain: $( 0 , \infty )$; range: $( \infty , \infty )$
  
B)  domain: $( 0 , \infty )$; range: $( \infty , \infty )$
  
C)  domain: $( \infty , \infty )$; range: $( 0 , \infty )$
  
D)  domain: $( \infty , \infty )$; range: $( \infty , 0 )$
  
A)  domain: $( 0 , \infty )$; range: $( \infty , \infty )$
  
B)  domain: $( 0 , \infty )$; range: $( \infty , \infty )$
  
C)  domain: $( \infty , \infty )$; range: $( 0 , \infty )$
  
D)  domain: $( \infty , \infty )$; range: $( \infty , 0 )$

Question 20

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or
reflected.
-

Accepted Answer

A)  $\log _ { 2 } ( - x + 1 )$ 
B)  $- \log _ { 2 } ( x + 1 )$ 
C)  $- \log _ { 2 } ( x - 1 )$ 
D)  $- \log _ { 2 } ( - x - 1 )$ 
A)  $\log _ { 2 } ( - x + 1 )$ 
B)  $- \log _ { 2 } ( x + 1 )$ 
C)  $- \log _ { 2 } ( x - 1 )$ 
D)  $- \log _ { 2 } ( - x - 1 )$

Evaluate the logarithm. - $\log _ { 5 } 5$

Choose the one alternative that best completes the statement or answers the question. -A certain radioactive isotope decays at a rate of $0.2 \%$ annually. Determine the half-life of this isotope, to the nearest year.

Use properties of logarithms to evaluate the expression. -If $f ( x ) = e ^ { x }$ , find $f \left[ \ln \left( \frac { 1 } { e ^ { 2 } } \right) \right]$

Graph the exponential function using transformations where appropriate. - $f ( x ) = - 4 ^ { x - 1 }$ $Graph the exponential function using transformations where appropriate. - f ( x ) = - 4 ^ { x - 1 }$

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or reflected. -

Evaluate the logarithm. - $\log _ { 8 } 512$

Use the alphabet coding method (A =1, B = 2, C = 3, ... Z = 26) to -The function defined by $f ( x ) = 3 x - 4$ was used to encode a message as: 38 11 62 11 50 -1 17 -1 23 38 Find the inverse function and determine the message.

Write in logarithmic form. - $10 ^ { - 5 } = 0.00001$

Use a graphing calculator to graph the function using the given viewing window. Use the graph to decide if the function is one-to-one. If the function is one-to-one, give the equation of the inverse function. - $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - x + 3 ; [ - 2,4 ]$ by $[ - 20,20 ]$

Graph the exponential function using transformations where appropriate. - $f(x)=\left(\frac{1}{5}\right)^{x}+2$ $Graph the exponential function using transformations where appropriate. - f(x)=\left(\frac{1}{5}\right)^{x}+2$

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or reflected. -

Solve the equation. Give the answer in exact form. - $e ^ { 2 x } - 9 e ^ { x } + 20 = 0$

Decide whether the given functions are inverses. - f=\{(-3,-5),(1,3),(3,-3),(7,11)\} g=\{(-5,-3),(3,1),(-3,3),(11,7)\}

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $\mathrm { e } ^ { \mathrm { x } + \ln 3 = 2 \mathrm { e } ^ { \mathrm { x } } }$

Graph the function. Give the domain and range. - $f ( x ) = \log _ { 1 / 8 } x$ $Graph the function. Give the domain and range. - f ( x ) = \log _ { 1 / 8 } x$

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or reflected. -

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 5: Inverse, Exponential, and Logarithmic Functions

Evaluate the logarithm. - log⁡55\log _ { 5 } 5log5​5

Choose the one alternative that best completes the statement or answers the question. -A certain radioactive isotope decays at a rate of 0.2%0.2 \%0.2% annually. Determine the half-life of this isotope, to the nearest year.

Use properties of logarithms to evaluate the expression. -If f(x)=exf ( x ) = e ^ { x }f(x)=ex , find f[ln⁡(1e2)]f \left[ \ln \left( \frac { 1 } { e ^ { 2 } } \right) \right]f[ln(e21​)]

Graph the exponential function using transformations where appropriate. - f(x)=−4x−1f ( x ) = - 4 ^ { x - 1 }f(x)=−4x−1

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or reflected. -

Evaluate the logarithm. - log⁡8512\log _ { 8 } 512log8​512

Use the alphabet coding method (A =1, B = 2, C = 3, ... Z = 26) to -The function defined by f(x)=3x−4f ( x ) = 3 x - 4f(x)=3x−4 was used to encode a message as: 38 11 62 11 50 -1 17 -1 23 38 Find the inverse function and determine the message.

Write in logarithmic form. - 10−5=0.0000110 ^ { - 5 } = 0.0000110−5=0.00001

Graph the exponential function using transformations where appropriate. - f(x)=(15)x+2f(x)=\left(\frac{1}{5}\right)^{x}+2f(x)=(51​)x+2

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or reflected. -

Solve the equation. Give the answer in exact form. - e2x−9ex+20=0e ^ { 2 x } - 9 e ^ { x } + 20 = 0e2x−9ex+20=0

Decide whether the given functions are inverses. - f=\{(-3,-5),(1,3),(3,-3),(7,11)\} g=\{(-5,-3),(3,1),(-3,3),(11,7)\}

Solve the following graphically. If necessary, round answers to the nearest thousandth. - ex+ln⁡3=2ex\mathrm { e } ^ { \mathrm { x } + \ln 3 = 2 \mathrm { e } ^ { \mathrm { x } } }ex+ln3=2ex

Graph the function. Give the domain and range. - f(x)=log⁡1/8xf ( x ) = \log _ { 1 / 8 } xf(x)=log1/8​x

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or reflected. -

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Evaluate the logarithm. - $\log _ { 5 } 5$

Choose the one alternative that best completes the statement or answers the question. -A certain radioactive isotope decays at a rate of $0.2 \%$ annually. Determine the half-life of this isotope, to the nearest year.

Use properties of logarithms to evaluate the expression. -If $f ( x ) = e ^ { x }$ , find $f \left[ \ln \left( \frac { 1 } { e ^ { 2 } } \right) \right]$

Graph the exponential function using transformations where appropriate. - $f ( x ) = - 4 ^ { x - 1 }$ $Graph the exponential function using transformations where appropriate. - f ( x ) = - 4 ^ { x - 1 }$

Evaluate the logarithm. - $\log _ { 8 } 512$

Use the alphabet coding method (A =1, B = 2, C = 3, ... Z = 26) to -The function defined by $f ( x ) = 3 x - 4$ was used to encode a message as: 38 11 62 11 50 -1 17 -1 23 38 Find the inverse function and determine the message.

Write in logarithmic form. - $10 ^ { - 5 } = 0.00001$

Graph the exponential function using transformations where appropriate. - $f(x)=\left(\frac{1}{5}\right)^{x}+2$ $Graph the exponential function using transformations where appropriate. - f(x)=\left(\frac{1}{5}\right)^{x}+2$

Solve the equation. Give the answer in exact form. - $e ^ { 2 x } - 9 e ^ { x } + 20 = 0$

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $\mathrm { e } ^ { \mathrm { x } + \ln 3 = 2 \mathrm { e } ^ { \mathrm { x } } }$

Graph the function. Give the domain and range. - $f ( x ) = \log _ { 1 / 8 } x$ $Graph the function. Give the domain and range. - f ( x ) = \log _ { 1 / 8 } x$