# Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

3 Pages

### lgrulesl

Course: MATH 119, Spring 2009
School: illinoisstate.edu
Rating:

Word Count: 930

#### Document Preview

Rules Logarithm Worksheet Solutions NAME: Remember to think of log b x as the number to which I raise b to get x. This is very important in the study of logs. Let b, v, and w be positive real numbers where b is not equal to one. Let k be a real number. 1. In words, what is log b b ? It's the number to which I raise __b___ to get __b___. What does this number we call log b b have to be? Any number raised to 1 is...

Register Now

#### Unformatted Document Excerpt

Coursehero

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
Rules Logarithm Worksheet Solutions NAME: Remember to think of log b x as the number to which I raise b to get x. This is very important in the study of logs. Let b, v, and w be positive real numbers where b is not equal to one. Let k be a real number. 1. In words, what is log b b ? It's the number to which I raise __b___ to get __b___. What does this number we call log b b have to be? Any number raised to 1 is itself. The number you raise b to, to get itself, has to be 1. So log b b = 1 . 2. In words, what is log b 1 ? It's the number to which I raise __b___ to get __1___. What does this number we call log b 1 have to be? Any number raised to 0 is 1. The number you raise b to, to get 1, has to be 0. So log b 1 = 0 . 3. In words, what is log b (b k ) ? It's the number to which I raise __b___ to get __bk___. What does this number we call log b (b k ) have to be? This is sort of a trick question. What do I raise 2 to, to get 23 ? (Well, 3, silly. Don't ask stupid questions.) So, what do we raise b to, to get bk? (Well, k, silly. I told you not to ask stupid questions.) So log b (b k ) = k . 4. Now log b v is the number to which I raise b to get v. Therefore b raised to this power log b v or should be what number? b We have to hold in our head that log b v is the number to which I raise b to get v. This is crucial. See this " log b v " as one entity. It's the number I log b v raise b to, to get v. Now, when we write , we have taken b and log b v raised it this number. I should get v. So . We can also see log1 0 1000 this be looking at specific examples. We see that 10 = 10 3 = 1000 . b b =v 5. Complete the table. log 3 3 = 1 log 5 25 = 2 log 3 9 = log 5 5 = 2 1 2 log 3 27 = log 5 125 = 3 3 6 log 2 16 = 4 log 2 4 = log 2 64 = Now use the three rows of the table to determine the relationship between log b v , log b w , and log b (vw) . Write the rule down and then show it works using an example from the table. In the first row of the table, notice how we have the log of 3, the log of 9, and the log of their product 27. The second row finds the log of 25, the log of 5, and the log of their product 125. This is true of the third row too. What is the connection between (first row answers) 1 and 2, and 3? What is the connection between (third row answers) 4 and 2, and 6? We notice if we add the first two columns, we get the third column. So we see the rule emerge: log b (v ) + log b ( w) = log b ( vw) . As an example, log 2 16 + log 2 4 = log 2 64 . This is one of many the rules we will use to manipulate logs. 6. Complete the table. log 3 27 = 3 log 5 125 = 3 log 3 9 = 2 log 5 25 = 2 2 log 3 3 = 1 log 5 5 = 1 4 log 2 64 = 6 log 2 4 = log 2 16 = Now use the three rows of the table to determine the relationship between log b v , v log b w , and log b ( ) . Write the rule down and then show it works using an example w from the table. The reasoning is similar to that used above. The rule we are after is v log b (v ) - log b (w) = log b ( ) . As an example, log 2 64 - log 2 4 = log 2 16 . w 7. Complete the table. You may use your calculator for the first two. Round your answers to three decimal places. The last one you should be able to work out logically. log 35 = log e 6 2 = log 5 5 2 = ( ) 2.386 3.584 2 5 * log 3 = 2.386 3.584 2 ( ) ( ) 2 * log e 6 = 2 * log 5 5 = Now use the three rows of the table to determine the relationship between log b v k and k log b v . Write the rule down and then show it works using an example from the table. To find log 5 (5 2 ) by hand, use the rule developed in #3. To find 2 * log 5 5 , find log 5 5 and then multiply by 2. You should see that, for each example above, log b v k = k log b v . As an example, log 5 (5 2 ) = 2 * log 5 5 . Additional note concerning rules log b (b k ) = k and b log b v = v : These two rules are true because of the inverse relationship between the exponential function f ( x ) = b x and the logarithmic function g ( x) = log b ( x ) . Recall inverse functions undo each other....

Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

illinoisstate.edu - MATH - 119
Working with exponential functionsNAME:1. Complete the table. Then plot and connect the points to form a graph of f ( x ) = 3 x . x -2 f (x ) = 3 x-10122. Complete the table. Then plot and connect the points to form a graph of f ( x ) = 1 3 . x -2
illinoisstate.edu - MATH - 119
Solving equations using inversesNAME:For each function, complete the following steps in the spaces provided. -Describe the function in words. What we do to an x to get a y? -Find the function's inverse. Do not simplify as you go. -Describe the inverse i
illinoisstate.edu - MATH - 119
Inverses of functions 2NAME:1. Complete the table. Then plot the points (and connect them) to create a graph of the relationship y = .5( x - 2) 2 - 3 . x -4 y = .5( x - 2) 2 - 3-2024682. Describe in words the rule that assigns a y value to each x
illinoisstate.edu - MATH - 119
Exam 3 Practice resource: Answers and suggestions for study The italicized items are worksheets. The other items refer to the notes and book. Number 1 2 Answer B C Sections, worksheets to study Functions and Equations Part V, Three possibilities for a qua
illinoisstate.edu - MATH - 119
Math 119 NAME: Exam 3 Practice Functions and Equations Parts V VII, Advanced Functions and Equations Parts I and II 1.3, 1.6, 2.3, 2.4, 3.4, 3.5, 4.1, 4.2, 4.3, 4.4, 4.5, 5.3 This should give you an idea of what to expect on the exam. On the exam, you wil
illinoisstate.edu - MATH - 119
Math 119 Solutions to 4.5 homework 7.) Here we are looking for the x values that make x 2 + x &gt; 12 . So graph y = x 2 + x and y = 12 and see where the first graph is greater than (or above) y = 12 . The graph is below.The intersection points are at x = -
illinoisstate.edu - MATH - 119
Inequalities and you 3NAME:This worksheet will provide practice for solving absolute value, polynomial, and rational inequalities. We will also work on understanding why the procedures work. We will solve problems both algebraically and graphically. 1.
illinoisstate.edu - MATH - 119
Inequalities and you 3 SolutionsNAME:This worksheet will provide practice for solving absolute value, polynomial, and rational inequalities. We will also work on understanding why the procedures work. We will solve problems both algebraically and graphi
illinoisstate.edu - MATH - 119
Functions: Composition and operations SolutionsNAME:This worksheet will provide practice for adding, subtracting, dividing, and composing two functions. We will also investigate domains. 1. Let f ( x ) = 5x + 7 - 4 x and g ( x) = 5 x 2 + 7 x - 5 . Perfo
illinoisstate.edu - MATH - 119
Functions: Composition and operationsNAME:This worksheet will provide practice for adding, subtracting, dividing, and composing two functions. We will also investigate domains. 1. Let f ( x ) = 5x + 7 - 4 x and g ( x) = 5 x 2 + 7 x - 5 . Perform the des
illinoisstate.edu - MATH - 119
Polynomial functions: End behavior SolutionsNAME:In this lab, we are looking at the end behavior of polynomial graphs, i.e. what is happening to the y values at the (left and right) ends of the graph. In other words, we are interested in what is happeni
illinoisstate.edu - MATH - 119
Connection between polynomial and power functionsNAME:We will investigate how the end behavior of a polynomial function can be simplified by looking at its leading term. On this worksheet, it is not necessary to get too critical of your graphs; we are p
illinoisstate.edu - MATH - 119
Power functions: End behaviorNAME:We will investigate how we can tell the end behavior of a power function just by looking at its equation. Remember end behavior answers the question, &quot;what is happening to the y values as x gets really small (left end o
illinoisstate.edu - MATH - 119
Quadratic worksheet Maximums and minimumsNAME:We will investigate quadratic relationships whose graphs have maximum or minimum y values. They are called local or relative maximums or minimums because, compared to other nearby points, they have the large
illinoisstate.edu - MATH - 119
Quadratic functions: Maximums and minimums practiceNAME:1. Without graphing, determine the vertex of the function f ( x ) = 3x 2 - 5 x + 8 . Remember the vertex is a point; write it in ordered pair notation.2. Use your calculator to graph f ( x ) = 3x
illinoisstate.edu - MATH - 119
Quadratic functions Solutions : Maximums and minimums practiceNAME:1. Without graphing, determine the vertex of the function f ( x ) = 3x 2 5 x + 8 . Remember the vertex is a point; write it in ordered pair notation.x= b 5 5 = = = .83 2a 2 3 6f (.83)
illinoisstate.edu - MATH - 119
Quadratic functions practice SolutionsNAME:For questions 1 through 3, determine the functions orientation, y- intercept, and vertex (without graphing). Remember, a vertex has an x and a y value. Then provide a quick sketch of the parabola. Show your wor
illinoisstate.edu - MATH - 119
Three possibilities for a quadratic equation SolutionsNAME:This worksheet investigates an example of each of the three possibilities for a quadratic equation. For any quadratic equation, there could be zero, one, or two real solutions. In the case where
illinoisstate.edu - MATH - 119
Three possibilities for a quadratic equationNAME:This worksheet investigates an example of each of the three possibilities for a quadratic equation. For any quadratic equation, there could be zero, one, or two real solutions. In the case where there are
illinoisstate.edu - MATH - 119
Manipulating Complex Numbers 2 SolutionsNAME:This worksheet continues working on adding, subtracting, and multiplying complex numbers. Complex numbers like 3 + 2i are dealt with in the same way as numbers like 3 + 2x. We will also get practice checking
illinoisstate.edu - MATH - 119
Manipulating Complex Numbers 2NAME:This worksheet continues working on adding, subtracting, and multiplying complex numbers. Complex numbers like 3 + 2i are dealt with in the same way as numbers like 3 + 2x. We will also get practice checking complex so
illinoisstate.edu - MATH - 119
Manipulating complex numbers SolutionsNAME:This worksheet will work on understanding and manipulating complex numbers. Remember, well see complex numbers as solutions to quadratic equations with negative discriminants. They will be added, subtracted, an
illinoisstate.edu - MATH - 119
Manipulating complex numbersNAME:This worksheet will work on understanding and manipulating complex numbers. Remember, we'll see complex numbers as solutions to quadratic equations with negative discriminants. They will be added, subtracted, and multipl
illinoisstate.edu - MATH - 119
TI83 Quadratic Formula Program QUADRATC :ClrHome :Full :Func :Float :1Xscl :1Yscl :Outpt(1,1,GRAPHICAL :Outpt(2,4,QUADRATIC :Outpt(3,8,EQUATIONS :Outpt(5,1,AX2 + BX + C = 0 :Outpt(7,3,TO CONTINUE, :Outpt(8,3,PRESS ENTER. :Pause :ExprOff :FnOff : AX2 +BX+C
illinoisstate.edu - MATH - 119
TI86 Quadratic Formula Program QUAD2 :CILCD :Func :Float :1xScl :1yScl :Outpt(1,1,GRAPHICAL :Outpt(2,4,QUADRATIC :Outpt(3,8,EQUATIONS :Outpt(5,1,AX2 + BX + C = 0 :Outpt(7,3,TO CONTINUE, :Outpt(8,3,PRESS ENTER. :Pause :FnOff :y1=Ax2 +Bx+C :Lbl A1 :CILCD :O
illinoisstate.edu - MATH - 119
Using the Program QUAD2 (TI86 and TI85) or QUADRATC (TI82 or TI83) Let's say we want to solve the equation 0 = 3x 2 + 5 x - 6 . Recall the solutions to this equation are also the x-intercepts of the function y = 3 x 2 + 5 x - 6 . This program will reinfor
illinoisstate.edu - MATH - 119
Link instructions for the TI calculators 1. Connect the link cable between two calculators. Make sure the plugs are firmly seated. 2. Press 2nd and the X, T, , n button. (It's X, T, on the TI82. It's x-VAR on the TI85 or 86.) The second function of this b
illinoisstate.edu - MATH - 119
Discriminants and x-intercepts SolutionsNAME:There are three possibilities for the number of x-intercepts of a quadratic function: two, one, or zero. Fill in the following table to develop examples for these three possibilities. Choose small enough va l
illinoisstate.edu - MATH - 119
Quadratic equations practice SolutionsNAME:1. We will investigate the relationship described by the online problem &quot;Can you figure the initial velocity of the ball?&quot; found under the Problems section of the Website. The equation s = -16t 2 + v0 t + s0 de
illinoisstate.edu - MATH - 119
Quadratic equations practiceNAME:1. We will investigate the relationship described by the online problem &quot;Can you figure the initial velocity of the ball?&quot; found under the Problems section of the Website. The equation s = -16t 2 + v0 t + s0 describes th
illinoisstate.edu - MATH - 119
Quadratic functions Orientation, vertex, and y- intercept SolutionsNAME:1. y-intercept: The y- intercept of any function is found by substituting 0 in for x. This works because the x value of every point on the y-axis is 0. Youre simply using this fact
illinoisstate.edu - MATH - 119
Exam 2 Practice resource: Answers and suggestions for study The italicized items are worksheets. The other items refer to the notes and book. Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Answer D E B D A E A D C E C A B E B Sections, worksheets to study The
illinoisstate.edu - MATH - 119
Quadratic functions Orientation, vertex, and y- interceptNAME:1. y-intercept: The y- intercept of any function is found by substituting 0 in for x. This works because the x value of every point on the y-axis is 0. Youre simply using this fact along with
illinoisstate.edu - MATH - 119
!&quot;! ## % ( + ! ' ) '\$&amp; &quot;!' #* * #*%% #! &quot; \$!&quot;,, ! &quot; % &amp; ) &quot; # \$-)'\$* #)## +)#+ ! . !) ' 0(&quot; ! .# &amp; ' \$ !# \$ 0) #/ * ) *'!!# ( )&quot;' ! &amp;#&quot;# ) &quot;\$&amp;, + ! . !) ' 1 0(&quot; ! .# &amp; ' \$ !# \$ 0) #/ * ) ** * ' !** * !# ( *) *
illinoisstate.edu - MATH - 119
Linear function applicationsNAME:These problems involve variables that are linearly related, meaning their graphs will be straight lines. Draw the graphs using a straight edge. 1. You produce exotic candles. You have up-front costs of \$25 (perhaps the r
illinoisstate.edu - MATH - 119
!&quot; \$ &amp; '#\$ % \$ '&quot; \$ &amp; '&amp; ( ) &quot;\$&quot; \$ &amp; '% * &quot;% \$&quot; \$ &amp; '* ( ' \$+,+ , !+ &quot;0 ! ! . 3. 1 2 .. ./&quot; \$ &amp; '#\$ % \$ '# 4\$ 4\$ 4\$ % #! &quot;&quot;# # \$# &amp;&quot; \$ &amp; '&amp; ( ) &quot;\$#' &quot; \$ &amp; ' % * &quot;% \$ # ( &amp; ) #&quot; \$ &amp; ' ! .* ( ' \$# ! ! !!56 / ! ! 0 765&amp; +!&quot;%-
illinoisstate.edu - MATH - 119
Understanding slopeNAME:This worksheet will work on some preliminary information we need to understand linear functions. For each table below, use the graph paper directly below to plot the points. x 1 2 3 4 y -2 0 2 4 x 1 2 3 4 y 3 6 9 12x 1 2 3 4y 0
illinoisstate.edu - MATH - 119
Solving absolute value and radical equations SolutionsNAME:This worksheet is designed to help you make sense of some of the methods we use to solve absolute value and radical equations algebraically. We will also look at solving these equations graphica
illinoisstate.edu - MATH - 119
Solving absolute value and radical equationsNAME:This worksheet is designed to help you make sense of some of the methods we use to solve absolute value and radical equations algebraically. We will also look at solving these equations graphically. 1a. C
illinoisstate.edu - MATH - 119
! # &quot; # '% &quot;. '%&amp; \$%&quot; +% -%# ( )* , ( )*\$%&amp; &quot;/ )*0 / &quot; (#, 1 &quot; 1( 32 / / 6 2/2 1 \$* \$%&amp; '%&amp;3 4 / 32 3! \$*0 / 5 ( 3-*\$*= '*&amp;7 5 6((! # \$ %&amp;&quot; &quot; '()&quot;1(, 1()* '*0 # ( ( 9% '* / \$*\$* 7#82 = ') -+&amp;3* # &quot;+ ) , # \$ ! - . / \$ %&amp; / '(
illinoisstate.edu - MATH - 119
Increasing and decreasing functions SolutionsNAME:The function f(x) is shown below. Complete the table by finding the f(x) values for the given values of x. The points are plotted to help you. Round to the nearest whole number.x -10f(x) 12 5x 0f(x)
illinoisstate.edu - MATH - 119
Mixture problems: Salt concentrationNAME:This worksheet will help us understand mixture problems that involve combining liquids of different concentrations to form a final mixture of another concentration. Consider two salt solutions, Solution A and Sol
illinoisstate.edu - MATH - 119
Story problems practiceNAME:Remember to define your variable specifically. Write a verbal model before you attempt to form an equation. Then form the equation and solve it. Circle and label your final answer. 1. Blane has a paper route which he can fini
illinoisstate.edu - MATH - 119
Story problems are my friendsNAME:We will practice solving story problems. The rough steps are outlined for each problem. Remember, always create a verbal model before you try to form an equation. It's also very important to define your variable specifi
illinoisstate.edu - MATH - 119
Story Problem Pieces SolutionsNAME:The purpose of this worksheet is to practice using algebraic notation to represent real world ideas. For instance, if w is the width of a rectangle, and the length is twice the width, give an expression for the length.
illinoisstate.edu - MATH - 119
Investigating functions 2 SolutionsNAME:This worksheet will work on interpreting functional notation, determining function values, and determining the domain and range of functions. 1. For each equation or graph, find the desired value(s). Estimates wil
illinoisstate.edu - MATH - 119
Investigating functions 2NAME:This worksheet will work on interpreting functional notation, determining function values, and determining the domain and range of functions. 1. For each equation or graph, find the desired value(s). Estimates will be accep
illinoisstate.edu - MATH - 119
Exam 1 Practice resource: Answers and suggestions for study The italicized items are worksheets. The other items refer to the notes and book. Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Answer B B C D E A D B C C E A B D E Sections, worksheets to study The
illinoisstate.edu - MATH - 119
Investigating functionsNAME:This worksheet will help us practice the basic idea of a function and functional notation. 1. For each of the following graphs or equations, tell whether or not the relationship is a function. If it is not a function, give an
illinoisstate.edu - MATH - 119
Inequalities and you 1 SolutionsNAME:This worksheet will provide practice for solving and interpreting inequalities. We will first investigate the general rules for algebraically solving inequalities. We will then solve a few problems algebraically. 1.
illinoisstate.edu - MATH - 119
Inequalities and you 1NAME:This worksheet will provide practice for solving and interpreting inequalities. We will first investigate the general rules for algebraically solving inequalities. We will then solve a few problems algebraically. 1. Show that
illinoisstate.edu - MATH - 119
Inequality Practice Problems Solutions Solve the following inequalities. Write your answer in interval notation. 1. 5x - 8 &gt; 12 5x &gt; 20 x&gt;4 (4, ) Here, x was multiplied by 5, then 8 was subtracted to get it to be greater than 12. So undo that by adding 8
illinoisstate.edu - MATH - 119
Solve the following inequalities. Write your answer in interval notation. 1. 5 x 8 &gt; 12 2. 4(5 2 x ) 132x 4 3&lt; &lt; 10 3. 7
illinoisstate.edu - MATH - 119
Solve the following equations by factoring. Solutions 1. I used the AC method to factor the left side. 2 Once you're at the (x - 5)(3x + 2) = 0 stage, 3 x - 13 x - 10 = 03 x - 15 x + 2 x - 10 = 023 x ( x - 5 ) + 2( x - 5) = 0( x - 5)(3 x + 2) = 0 x -5
illinoisstate.edu - MATH - 119
Solve the following equations by factoring. 1. 3x 13 x 10 = 022. (2 x 1)(x + 1) = 023. ( x + 3) = 92
illinoisstate.edu - MATH - 119
Solving equationsNAME:The point of solving an equation is to find the value(s) of the variable that make the equation true. This worksheet focuses on undoing what was done to the variable in order to uncover it. For instance, let's say we want to solve
illinoisstate.edu - MATH - 119
Solving equations SolutionsNAME:The point of solving an equation is to find the value(s) of the variable that make the equation true. This worksheet focuses on undoing what was done to the variable in order to uncover it. For instance, let's say we want
illinoisstate.edu - MATH - 119
Carchip Worksheet SolutionsNAME:The following graph is a simplified version of the graph generated by the Carchip module. It shows the relationship between the speed of a car and time. Answer the questions. We will then investigate the real Carchip grap
illinoisstate.edu - MATH - 119
Carchip WorksheetNAME:The following graph is a simplified version of the graph generated by the Carchip module. It shows the relationship between the speed of a car and time. Answer the questions. We will then investigate the real Carchip graphs.1. Des
illinoisstate.edu - MATH - 119
TI86 or TI85 Distance and midpoint program DIST2 :Disp &quot;ENTER FIRST X&quot; :Input A :Disp &quot;ENTER FIRST Y&quot; :Input B :Disp &quot;ENTER SECOND X&quot; :Input C :Disp &quot;ENTER SECOND Y&quot; :Input D :ClLCD : ( A - C ) 2 + ( B - D) 2 ) F :Disp &quot;DISTANCE=&quot; :Disp F :(A+C)/2I :(B+D)
illinoisstate.edu - MATH - 119
TI83 or TI82 Distance and midpoint program DIST2 :Disp ENTER FIRST X :Input A :Disp ENTER FIRST Y :Input B :Disp ENTER SECOND X :Input C :Disp ENTER SECOND Y :Input D :ClrHome : ( A C ) 2 + ( B D) 2 ) F :Disp DISTANCE= :Disp F :(A+C)/2I :(B+D)/2J :Disp MI