Geology geomathematics. Earthquakes log and exponential relationships
|
|
- Jasper Anderson
- 5 years ago
- Views:
Transcription
1 Geology geomathematics Earthquakes log and exponential relationships tom.h.wilson tom.wilson@mail.wvu.edu Department of Geology and Geography West Virginia University Morgantown, WV
2 Objectives for the day Learn to use the frequency-magnitude model to estimate recurrence intervals for earthquakes of specified magnitude and greater. Frequency magnitude and microseismic Learn how to express exponential functions in logarithmic form (and logarithmic functions in exponential form).
3 World seismicity one week view
4 IRIS Seismic Monitor
5 Lists of data in the area you select are also available if you d like to do your own analysis
6 Magnitude distribution 300 Earthquake magnitudes histogram January 13-20, Number Magnitude
7 Number of earthquakes per year Number of earthquakes per year of Magnitude m and greater Some worldwide data m N/year Observational data for earthquake magnitude (m) and frequency (N, number of earthquakes per year (worldwide) with magnitude m and greater) Richter Magnitude What would this plot look like if we plotted the log of N versus m?
8 log(n) The Gutenberg-Richter Relationship or frequency-magnitude relationship Number of earthquakes per year log N bm -b is the slope and c is the intercept. c Richter Magnitude
9 Let s determine N for a magnitude 7.2 quake. 3 Frequency (log10n) Magnitude Plot (Haitian Region) Log 10 N 2 1 logn= m log N 0.935m 5.21 log N 0.935(7.2) 5.21 log N Magnitude N=10 logn = This is number of earthquakes of magnitude m and greater per year.
10 The recurrence time Log 10 N Frequency (log10n) Magnitude Plot (Haitian Region) 3 2 logn= m Magnitude To estimate the recurrence interval, simply compute 1/N. This result has units of years and provides an estimate of the number of years between magnitude 7.2 and greater (or m and greater in general) earthquakes in the region.
11 Earthquakes on a different scale - microseismicity associated with hydraulic fracture treatment Downie, R., Kronenberger, Carizo, Maxwell, 2912, SPE
12 Shear along old dead fractures in the area near the well bore
13 Hydraulic fracture stimulation produces a lot of microseismic activity
14 Microseismicity from the top well
15 out-of-zone events Critically stressed ready-to-break area.
16 From Kanamori (1977) & also Boroumond and Eaton (2012) Another area where logarithms and their manipulation become useful log ( E ) 1.5M s M o is moment magnitude. The constant 4.8 gives E in Joules. As an independent exercise determine this constant for E(ergs) To calculate E we have to take the exponential inverse of the log. Can you do it? See slides near the end of todays set. o Tom Wilson, Department of Geology and Geography
17 Energy equivalents from an IHS webinar
18 Record of pump pressure & microseismicity
19 Injection pressure compared to lithostatic Sv z ( z) gdz 0
20 In some cases microseismic activity continues after pumping is completed
21 We can also undertake frequency-magnitude analysis of microseismic data Some authors suggest that b~1 implies reactivation of pre-existing faults Downie, R., Kronenberger, Carizo, Maxwell, 2912, SPE
22 And that stimulation of smaller natural fractures in the reservoir results in higher b-value (slope) Downie, R., Kronenberger, Carizo, Maxwell, 2912, SPE
23 A Marcellus frac. Treatments proceeds from toe to heel Heel Toe
24 b-values along well #1 Toe Heel
25 Another application See 2/313_GC2012_Comparing_Energy_Calculations.pdf For applications to microseismic events produced during frac ing. Missing data or how many events didn t you hear?
26 Rupture area associated with microseismic events is very small Zoback, 2014, online geomechanics class
27 Earthquakes associated with brine disposal have much larger magnitude Zoback, 2014, online geomechanics class
28 Back to class example, you know b from analysis of the data. How do you solve for N 7.2? What is N 7.2? log N 0.935m 5.21 log N 0.935(7.2) log N Let s discuss logarithms for a few minutes and come back to this later.
29 Any questions about logarithms? Logarithms are based (initially) on powers of 10. We know for example that 10 0 =1, 10 1 = = =1000 And negative powers give us 10-1 = = =0.001, etc.
30 Remember the general definition of a log The logarithm of y - i.e. log(y) =x solves the equation 10 x or 10 log(y) = y The logarithm of y is the exponent (x) we have to raise 10 to - to get y. So log (y=1000) = 3 since 10 3 = 1000 & log (10 y ) = y since Check your understanding on these slides else got to slide 36
31 Questions? - more review examples What is log 10? We rewrite this as log (10) 1/2. Since we have to raise 10 to the power ½ to get 10, the log is just ½. Some other general rules to keep in mind are that log (xy)=log x + log y log (x/y)= log x log y log x n =n log x
32 Remember the exponential functions have the independent variable in the exponent So you are dealing with equations like the following: cx y ab y a10 or cx Where b and 10 are the bases. These are constants and we can define any other number in terms of these constants and base raised to a certain power.
33 For any number y, we can write x y 10 By definition, we also say that x is the log of y, and can write log y x log 10 x So the powers of the base are the logs, and when asked what is log y, wherey 45 We assume that we are asking for x such that x 10 45
34 Many suggest that the base always be specified log 10 y, wherey 45 log 10 y leaves no room for doubt that we are specifically interested in the log for a base of 10. One of the confusing things about logarithms is the word itself. What does it mean? You might read log 10 y to say - What is the power that 10 must be raised to to get y? How about this operator? - pow y 10
35 pow y 10 The power of base 10 that yields ( ) y pow10 45 = What power do we have to raise the base 10 to, to get 45 log 10 y pow10 45 = 1.653
36 We ve already worked with three bases: 2, 10 and e. Whatever the base, the logging operation is the same. log5 10 asks what is the power that 5 must be raised to, to get 10. x log 10 x where How do we find these powers? 10 log 5 log 510 thus log log
37 In general, log base (some number) log b a or log log ( a) b Try the following on your own log 10( number ) log base 10 log10(7) log 3 7 log (3) 10? log 8 8 log 7 21 log 4 7
38 Helpful way to remember how to determine the power for an arbitrary base say n, where log (y) b Put this in exponential form Take the log base 10 of this expression and solve for x Take the log 10 of both sides of this equation to get the general rule that Otherwise stated as x x x b log 10( y) log (b) log (the number) log (base) 10 x y
39 log10 is often written as log, with no subscript log 10 is referred to as the common logarithm log is often written as ln. e log e 8 thus ln log e or ln is referred to as the natural logarithm. All other bases are usually specified by a subscript on the log, e.g. log5 or log 2, etc.
40 Return to the problem developed earlier log N 0.935m 5.21 log N 0.935(7.2) 5.21 log N 1.52 Where N, in this case, is the number of earthquakes of magnitude 7.2 and greater per year that occur in this area. How do you calculate N and what does it mean?
41 Solution review Since log N 1.52 N is the power you have to raise 10 to to get N. Take another example: given b = 1.25 and c=7, how often can a magnitude 8 and greater earthquake be expected? (don t forget to put the minus sign in front of b!) log N =.
42 Seismic energy-magnitude relationships more logs ( log 10 E s ) 1.5M 4.8 What energy is released by a magnitude 4 earthquake? A magnitude 5? Can you prove that the energy increases 31.6 times? More logs and exponents!
43 How would you solve for E? Where ( log 10 E s ) 1.5M 4.8 Hint 10 Es 10 log ( )
44 Basic notation reminders log(x) implies log 10 ln(x) implies log e When in doubt ask. Also, if different bases are in use, specify: i.e. log 10 (x), log 2 (x)
45 A question to think about Where z e o How would you solve for?
46 Have a look at the basics.xlsx file. See youtube video for brief overview of file contents Some of the worksheets are interactive allowing you to get answers to specific questions. Plots are automatically adjusted to display the effect of changing variables and constants Just be sure you can do it on your own!
47 Spend the remainder of the class working on Discussion group problems. The one below is all that will be due today
48 We ll save these for next time
49 Don t forget to hand in the group problems (set 2) from last time
50 In the next class, we will spend some time working with Excel.
51 Next Time Hand in group problems from last Thursday before leaving today. If completed, I ll pick up today s inclass work need more time? Look over problems 2.11 through 2.13 for discussion next time Continue reading text (everyone get a text?) We will examine a comprehensive approach to solving problems 2.11 and 2.13 using Excel next time.
Log relationships, trig functions, earthquakes & computer lab
Log relationships, trig functions, earthquakes & computer lab tom.h.wilson tom.wilson@mail.wvu.edu Department of Geoy and Geography West Virginia University Morgantown, WV Logarithms The allometric or
More informationBasic Review continued
Basic Review continued tom.h.wilson tom.wilson@mail.wvu.edu Department of Geology and Geography West Virginia University Morgantown, WV Previously Drew a correlation between basic mathematical representations
More informationBasic Review continued
Basic Review continued tom.h.wilson tom.wilson@mail.wvu.edu Department of Geology and Geography West Virginia University Morgantown, WV Previously Drew a correlation between basic mathematical representations
More informationPutting calculus concepts to work with some review
Geol 351 Geomath Putting calculus concepts to work with some review tom.h.wilson tom.wilson@mail.wvu.edu Dept. Geology and Geography West Virginia University Don t forget - Excel problem 9.7 due today!
More informationtom.h.wilson Dept. Geology and Geography West Virginia University
tom.h.wilson tom.wilson@mail.wvu.edu Dept. Geology and Geography West Virginia University Objectives for the day 8.13 and 8.14 due next time In-class digital approach to differentiation including simple
More informationGeology Geomathematics. Introduction to differential calculus part 2. tom.h.wilson
Geology 351 - Geomathematics Introduction to differential calculus part 2 tom.h.wilson tom.wilson@mail.wvu.edu Dept. Geology and Geography West Virginia University Last time Basic differentiation rules:
More informationtom.h.wilson Dept. Geology and Geography West Virginia University Tom Wilson, Department of Geology and Geography
tom.h.wilson tom.wilson@mail.wvu.edu Dept. Geology and Geography West Virginia University Items on the to do list Finish reading Chapter 8 and look over problems 8.13 and 8.14. Problems 8.13 and 8.14 are
More information#29: Logarithm review May 16, 2009
#29: Logarithm review May 16, 2009 This week we re going to spend some time reviewing. I say re- view since you ve probably seen them before in theory, but if my experience is any guide, it s quite likely
More informationGeology Geomathematics. An introduction to differential calculus. tom.h.wilson
Geology 351 - Geomathematics An introduction to differential calculus tom.h.wilson tom.wilson@mail.wvu.edu Dept. Geology and Geography West Virginia University Developing basic concepts and learning some
More informationMath 5a Reading Assignments for Sections
Math 5a Reading Assignments for Sections 4.1 4.5 Due Dates for Reading Assignments Note: There will be a very short online reading quiz (WebWork) on each reading assignment due one hour before class on
More informationAlgebra & Trig Review
Algebra & Trig Review 1 Algebra & Trig Review This review was originally written for my Calculus I class, but it should be accessible to anyone needing a review in some basic algebra and trig topics. The
More informationGeology Geomath. Practice with basic equation manipulation Using isostatic equilibrium relationships
Geology 351 - Geomath Practice with basic equation manipulation Using isostatic equilibrium relationships tom.h.wilson tom.wilson@mail.wvu.edu Department of Geology and Geography West Virginia University
More informationLogarithms and Exponentials
Logarithms and Exponentials Steven Kaplan Department of Physics and Astronomy, Rutgers University The Basic Idea log b x =? Whoa...that looks scary. What does that mean? I m glad you asked. Let s analyze
More information( )( b + c) = ab + ac, but it can also be ( )( a) = ba + ca. Let s use the distributive property on a couple of
Factoring Review for Algebra II The saddest thing about not doing well in Algebra II is that almost any math teacher can tell you going into it what s going to trip you up. One of the first things they
More informationEstimating energy balance for hydraulic fracture stimulations: Lessons Learned from Basel
Estimating energy balance for hydraulic fracture stimulations: Lessons Learned from Basel David W. Eaton*, Department of Geoscience, University of Calgary, Calgary, Canada eatond@ucalgary.ca and Neda Boroumand,
More informationLab Slide Rules and Log Scales
Name: Lab Slide Rules and Log Scales [EER Note: This is a much-shortened version of my lab on this topic. You won t finish, but try to do one of each type of calculation if you can. I m available to help.]
More informationWe ll start today by learning how to change a repeating decimal into a fraction! Then we will do a review of Unit 1 - half of Unit 3!
Welcome to math! We ll start today by learning how to change a repeating decimal into a fraction! Then we will do a review of Unit 1 - half of Unit 3! So grab a seat where you can focus, and get ready
More informationtom.h.wilson Department of Geology and Geography West Virginia University Morgantown, WV
Equation Manipulation illustrated around the concept of Isostacy tom.h.wilson tom.wilson@geo.wvu.edu Department of Geology and Geography West Virginia University Morgantown, WV Objectives for the day Hand
More informationPOLYNOMIAL EXPRESSIONS PART 1
POLYNOMIAL EXPRESSIONS PART 1 A polynomial is an expression that is a sum of one or more terms. Each term consists of one or more variables multiplied by a coefficient. Coefficients can be negative, so
More informationHow to use these notes
Chapter How to use these notes These notes were prepared for the University of Utah s Math 00 refresher course. They asssume that the user has had the Math 00 course Intermediate Algebra or its equivalent
More informationDerivatives: definition and computation
Math 10A September 6, 2016 Announcements The breakfasts tomorrow and Thursday are full, but there are spaces at the 8AM breakfast on September 13. This is a breakfast from last semester. The gentleman
More informationCalculus II. Calculus II tends to be a very difficult course for many students. There are many reasons for this.
Preface Here are my online notes for my Calculus II course that I teach here at Lamar University. Despite the fact that these are my class notes they should be accessible to anyone wanting to learn Calculus
More informationThermodynamics (Classical) for Biological Systems. Prof. G. K. Suraishkumar. Department of Biotechnology. Indian Institute of Technology Madras
Thermodynamics (Classical) for Biological Systems Prof. G. K. Suraishkumar Department of Biotechnology Indian Institute of Technology Madras Module No. #04 Thermodynamics of solutions Lecture No. #22 Partial
More information6.3 logarithmic FUnCTIOnS
SECTION 6.3 logarithmic functions 4 9 1 learning ObjeCTIveS In this section, you will: Convert from logarithmic to exponential form. Convert from exponential to logarithmic form. Evaluate logarithms. Use
More informationAlgebra Exam. Solutions and Grading Guide
Algebra Exam Solutions and Grading Guide You should use this grading guide to carefully grade your own exam, trying to be as objective as possible about what score the TAs would give your responses. Full
More informationSTANDARDS OF LEARNING CONTENT REVIEW NOTES. ALGEBRA I Part II 1 st Nine Weeks,
STANDARDS OF LEARNING CONTENT REVIEW NOTES ALGEBRA I Part II 1 st Nine Weeks, 2016-2017 OVERVIEW Algebra I Content Review Notes are designed by the High School Mathematics Steering Committee as a resource
More informationMAT137 - Term 2, Week 2
MAT137 - Term 2, Week 2 This lecture will assume you have watched all of the videos on the definition of the integral (but will remind you about some things). Today we re talking about: More on the definition
More informationGravity Methods (VII) more wrap up
Environmental and Exploration Geophysics II Gravity Methods (VII) more wrap up tom.h.wilson tom.wilson@mail.wvu.edu Department of Geology and Geography West Virginia University Morgantown, WV 0.4 0.35
More informationAlgebra. Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed.
This document was written and copyrighted by Paul Dawkins. Use of this document and its online version is governed by the Terms and Conditions of Use located at. The online version of this document is
More informationSeismicity of Northern California
Homework 4 Seismicity of Northern California Purpose: Learn how we make predictions about seismicity from the relationship between the number of earthquakes that occur and their magnitudes. We know that
More informationPage 1. These are all fairly simple functions in that wherever the variable appears it is by itself. What about functions like the following, ( ) ( )
Chain Rule Page We ve taken a lot of derivatives over the course of the last few sections. However, if you look back they have all been functions similar to the following kinds of functions. 0 w ( ( tan
More informationbase 2 4 The EXPONENT tells you how many times to write the base as a factor. Evaluate the following expressions in standard notation.
EXPONENTIALS Exponential is a number written with an exponent. The rules for exponents make computing with very large or very small numbers easier. Students will come across exponentials in geometric sequences
More informationtom.h.wilson Dept. Geology and Geography West Virginia University Tom Wilson, Department of Geology and Geography
tom.h.wilson tom.wilson@mail.wvu.edu Dept. Geology and Geography West Virginia University Graduation! Mark your calendars. For the day Strain Integration of discontinuous functions Acceleration due to
More informationIntroduction. So, why did I even bother to write this?
Introduction This review was originally written for my Calculus I class, but it should be accessible to anyone needing a review in some basic algebra and trig topics. The review contains the occasional
More informationMath101, Sections 2 and 3, Spring 2008 Review Sheet for Exam #2:
Math101, Sections 2 and 3, Spring 2008 Review Sheet for Exam #2: 03 17 08 3 All about lines 3.1 The Rectangular Coordinate System Know how to plot points in the rectangular coordinate system. Know the
More informationIdentifying fault activation during hydraulic stimulation in the Barnett shale: source mechanisms, b
Identifying fault activation during hydraulic stimulation in the Barnett shale: source mechanisms, b values, and energy release analyses of microseismicity Scott Wessels*, Michael Kratz, Alejandro De La
More informationA. Evaluate log Evaluate Logarithms
A. Evaluate log 2 16. Evaluate Logarithms Evaluate Logarithms B. Evaluate. C. Evaluate. Evaluate Logarithms D. Evaluate log 17 17. Evaluate Logarithms Evaluate. A. 4 B. 4 C. 2 D. 2 A. Evaluate log 8 512.
More informationSTANDARDS OF LEARNING CONTENT REVIEW NOTES. ALGEBRA I Part II. 2 nd Nine Weeks,
STANDARDS OF LEARNING CONTENT REVIEW NOTES ALGEBRA I Part II 2 nd Nine Weeks, 2016-2017 1 OVERVIEW Algebra I Content Review Notes are designed by the High School Mathematics Steering Committee as a resource
More informationAlgebra II. Slide 1 / 261. Slide 2 / 261. Slide 3 / 261. Linear, Exponential and Logarithmic Functions. Table of Contents
Slide 1 / 261 Algebra II Slide 2 / 261 Linear, Exponential and 2015-04-21 www.njctl.org Table of Contents click on the topic to go to that section Slide 3 / 261 Linear Functions Exponential Functions Properties
More informationPractice Questions for Final Exam - Math 1060Q - Fall 2014
Practice Questions for Final Exam - Math 1060Q - Fall 01 Before anyone asks, the final exam is cumulative. It will consist of about 50% problems on exponential and logarithmic functions, 5% problems on
More informationPre-Calculus Notes from Week 6
1-105 Pre-Calculus Notes from Week 6 Logarithmic Functions: Let a > 0, a 1 be a given base (as in, base of an exponential function), and let x be any positive number. By our properties of exponential functions,
More informationToward interpretation of intermediate microseismic b-values
Toward interpretation of intermediate microseismic b-values Abdolnaser Yousefzadeh, Qi Li, Schulich School of Engineering, University of Calgary, Claudio Virues, CNOOC- Nexen, and Roberto Aguilera, Schulich
More informationDifferentiation by taking logarithms
Differentiation by taking logarithms mc-ty-difftakelogs-2009-1 In this unit we look at how we can use logarithms to simplify certain functions before we differentiate them. In order to master the techniques
More informationDifferentiation by taking logarithms
Differentiation by taking logarithms In this unit we look at how we can use logarithms to simplify certain functions before we differentiate them. In order to master the techniques explained here it is
More informationBefore we do that, I need to show you another way of writing an exponential. We all know 5² = 25. Another way of writing that is: log
Chapter 13 Logarithms Sec. 1 Definition of a Logarithm In the last chapter we solved and graphed exponential equations. The strategy we used to solve those was to make the bases the same, set the exponents
More informationFinal Review session 2
Environmental and Exploration Geophysics I Final Review session 2 tom.h.wilson tom.wilson@mail.wvu.edu Department of Geology and Geography West Virginia University Morgantown, WV Reminders Turn in magnetics
More informationUnit 3 Day 4. Solving Equations with Rational Exponents and Radicals
Unit Day 4 Solving Equations with Rational Exponents and Radicals Day 4 Warm Up You know a lot about inverses in mathematics we use them every time we solve equations. Write down the inverse operation
More informationComputational Techniques Prof. Dr. Niket Kaisare Department of Chemical Engineering Indian Institute of Technology, Madras
Computational Techniques Prof. Dr. Niket Kaisare Department of Chemical Engineering Indian Institute of Technology, Madras Module No. # 07 Lecture No. # 04 Ordinary Differential Equations (Initial Value
More informationImplicit Differentiation Applying Implicit Differentiation Applying Implicit Differentiation Page [1 of 5]
Page [1 of 5] The final frontier. This is it. This is our last chance to work together on doing some of these implicit differentiation questions. So, really this is the opportunity to really try these
More informationThis format is the result of tinkering with a mixed lecture format for 3 terms. As such, it is still a work in progress and we will discuss
Version 1, August 2016 1 This format is the result of tinkering with a mixed lecture format for 3 terms. As such, it is still a work in progress and we will discuss adaptations both to the general format
More informationLecture 19: Introduction to Kinetics First a CH 302 Kinetics Study Guide (Memorize these first three pages, they are all the background you need)
Lecture 19: Introduction to Kinetics First a CH 302 Kinetics Study Guide (Memorize these first three pages, they are all the background you need) Reaction Rate: The most important issue in kinetics is
More informationMAS156: Mathematics (Electrical and Aerospace)
MAS156: Mathematics (Electrical and Aerospace) Dr Sam Marsh mas-engineering@sheffield.ac.uk Tuesday 17th October 2017, 1pm Diamond LT4 Course matters Online tests Some people had problems in the early
More informationEnvironmental and Exploration Geophysics I. Resistivity II tom.h.wilson
Environmental and Exploration Geophysics I Resistivity II tom.h.wilson tom.wilson@mail.wvu.edu Department of Geology and Geography West irginia University Morgantown, W For next class complete in-class
More informationSection 2.3: Logarithmic Functions Lecture 3 MTH 124
Procedural Skills Learning Objectives 1. Build an exponential function using the correct compounding identifiers (annually, monthly, continuously etc...) 2. Manipulate exponents algebraically. e.g. Solving
More informationWe ll start today by learning how to change a decimal to a fraction on our calculator! Then we will pick up our Unit 1-5 Review where we left off!
Welcome to math! We ll start today by learning how to change a decimal to a fraction on our calculator! Then we will pick up our Unit 1-5 Review where we left off! So go back to your normal seat and get
More information4.1 Solutions to Exercises
4.1 Solutions to Exercises 1. Linear, because the average rate of change between any pair of points is constant. 3. Exponential, because the difference of consecutive inputs is constant and the ratio of
More informationEngineering Mechanics Prof. Siva Kumar Department of Civil Engineering Indian Institute of Technology, Madras Statics - 5.2
Engineering Mechanics Prof. Siva Kumar Department of Civil Engineering Indian Institute of Technology, Madras Statics - 5.2 Now what we want to do is given a surface which is let s assume the surface is
More informationlog (N) 2.9<M< <M< <M< <M<4.9 tot in bin [N] = Mid Point M log (N) =
Solution Set for Assignment Exercise : Gutenberg-Richter relationship: log() = a + b. M A) For a time period between January, 90 to December 3, 998 tot in bin [] = 450 6 57 22 7 5 Mid Point M 3.5 3.65
More information3.5. Equation Solving and Modeling. Copyright 2011 Pearson, Inc.
3.5 Equation Solving and Modeling Copyright 2011 Pearson, Inc. What you ll learn about Solving Exponential Equations Solving Logarithmic Equations Orders of Magnitude and Logarithmic Models Newton s Law
More informationCHAPTER 7: TECHNIQUES OF INTEGRATION
CHAPTER 7: TECHNIQUES OF INTEGRATION DAVID GLICKENSTEIN. Introduction This semester we will be looking deep into the recesses of calculus. Some of the main topics will be: Integration: we will learn how
More informationDipping Layer Refraction Problem Moveout and Coincident Source-Receiver Format
Environmental and Exploration Geophysics II Dipping Layer Refraction Problem Moveout and Coincident Source-Receiver Format tom.h.wilson tom.wilson@mail.wvu.edu Department of Geology and Geography West
More informationPolynomial one or more monomials added or subtracted. (i.e. : 5x or 6xy-3 or 6xy - 5x + 3 or
Polynomials Necessary Terms for Success Welcome back! We will now tackle the world of polynomials. Before we get started with performing operations or using polynomials for applications, we will need some
More informationSimultaneous equations for circuit analysis
Simultaneous equations for circuit analysis This worksheet and all related files are licensed under the Creative Commons Attribution License, version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/,
More information[FILE] REWRITE EQUATION WITHOUT LOGARITHMS ARCHIVE
22 March, 2018 [FILE] REWRITE EQUATION WITHOUT LOGARITHMS ARCHIVE Document Filetype: PDF 493.97 KB 0 [FILE] REWRITE EQUATION WITHOUT LOGARITHMS ARCHIVE Note that writing log without the subscript. If we
More informationAn introduction to plotting data
An introduction to plotting data Eric D. Black California Institute of Technology v2.0 1 Introduction Plotting data is one of the essential skills every scientist must have. We use it on a near-daily basis
More informationGutenberg-Richter Relationship: Magnitude vs. frequency of occurrence
Quakes per year. Major = 7-7.9; Great = 8 or larger. Year Major quakes Great quakes 1969 15 1 1970 20 0 1971 19 1 1972 15 0 1973 13 0 1974 14 0 1975 14 1 1976 15 2 1977 11 2 1978 16 1 1979 13 0 1980 13
More informationRecitation Questions 1D Motion (part 1)
Recitation Questions 1D Motion (part 1) 18 January Question 1: Two runners (This problem is simple, but it has the same template as most of the problems that you ll be doing for this unit. Take note of
More informationMethods of Mathematics
Methods of Mathematics Kenneth A. Ribet UC Berkeley Math 10B April 19, 2016 There is a new version of the online textbook file Matrix_Algebra.pdf. The next breakfast will be two days from today, April
More informationBishop Kelley High School Summer Math Program Course: Honors Pre-Calculus
017 018 Summer Math Program Course: Honors Pre-Calculus NAME: DIRECTIONS: Show all work in the packet. Make sure you are aware of the calculator policy for this course. No matter when you have math, this
More informationSampling Distributions of the Sample Mean Pocket Pennies
You will need 25 pennies collected from recent day-today change Some of the distributions of data that you have studied have had a roughly normal shape, but many others were not normal at all. What kind
More informationSince the logs have the same base, I can set the arguments equal and solve: x 2 30 = x x 2 x 30 = 0
LOGARITHMIC EQUATIONS (LOGS) 1 Type 1: The first type of logarithmic equation has two logs, each having the same base, set equal to each other, and you solve by setting the insides (the "arguments") equal
More informationMathematical Background. e x2. log k. a+b a + b. Carlos Moreno uwaterloo.ca EIT e π i 1 = 0.
Mathematical Background Carlos Moreno cmoreno @ uwaterloo.ca EIT-4103 N k=0 log k 0 e x2 e π i 1 = 0 dx a+b a + b https://ece.uwaterloo.ca/~cmoreno/ece250 Mathematical Background Standard reminder to set
More informationDefinition of a Logarithm
Chapter 17 Logarithms Sec. 1 Definition of a Logarithm In the last chapter we solved and graphed exponential equations. The strategy we used to solve those was to make the bases the same, set the exponents
More information25 = 2. Remember to put the base lower than the g of log so you don t get confused 2. Write the log equation in exponential form 2.
LOGARITHMS The logarithm of a number to a given base is the exponent to which that base must be raised in order to produce the number. For example: What is the exponent that must be raised to in order
More informationEssentials of Intermediate Algebra
Essentials of Intermediate Algebra BY Tom K. Kim, Ph.D. Peninsula College, WA Randy Anderson, M.S. Peninsula College, WA 9/24/2012 Contents 1 Review 1 2 Rules of Exponents 2 2.1 Multiplying Two Exponentials
More informationChapter 5: Integrals
Chapter 5: Integrals Section 5.3 The Fundamental Theorem of Calculus Sec. 5.3: The Fundamental Theorem of Calculus Fundamental Theorem of Calculus: Sec. 5.3: The Fundamental Theorem of Calculus Fundamental
More informationSection 4.6 Negative Exponents
Section 4.6 Negative Exponents INTRODUCTION In order to understand negative exponents the main topic of this section we need to make sure we understand the meaning of the reciprocal of a number. Reciprocals
More informationGraphical Analysis and Errors MBL
Graphical Analysis and Errors MBL I Graphical Analysis Graphs are vital tools for analyzing and displaying data Graphs allow us to explore the relationship between two quantities -- an independent variable
More informationMath 138: Introduction to solving systems of equations with matrices. The Concept of Balance for Systems of Equations
Math 138: Introduction to solving systems of equations with matrices. Pedagogy focus: Concept of equation balance, integer arithmetic, quadratic equations. The Concept of Balance for Systems of Equations
More information3.4 Exponential and Logarithmic Equations
3.4 Exponential and Logarithmic Equations Pre-Calculus Mr. Niedert Pre-Calculus 3.4 Exponential and Logarithmic Equations Mr. Niedert 1 / 18 3.4 Exponential and Logarithmic Equations 1 Solving Simple Equations
More informationSolving Equations Quick Reference
Solving Equations Quick Reference Integer Rules Addition: If the signs are the same, add the numbers and keep the sign. If the signs are different, subtract the numbers and keep the sign of the number
More informationMAC 1105 Lecture Outlines for Ms. Blackwelder s lecture classes
MAC 1105 Lecture Outlines for Ms. Blackwelder s lecture classes These notes are prepared using software that is designed for typing mathematics; it produces a pdf output. Alternative format is not available.
More informationMATH 124. Midterm 2 Topics
MATH 124 Midterm 2 Topics Anything you ve learned in class (from lecture and homework) so far is fair game, but here s a list of some main topics since the first midterm that you should be familiar with:
More informationIf you have completed your extra credit opportunity, please place it on your inbox.
Warm-Up If you have completed your extra credit opportunity, please place it on your inbox. On everyone s desk should be paper and a pencil for notes. We are covering all of Quarter 1 in one day, so we
More informationSkill 6 Exponential and Logarithmic Functions
Skill 6 Exponential and Logarithmic Functions Skill 6a: Graphs of Exponential Functions Skill 6b: Solving Exponential Equations (not requiring logarithms) Skill 6c: Definition of Logarithms Skill 6d: Graphs
More information7.2 Logarithmic Functions Name: 1
Write your questions and thoughts here 7.2 Logarithmic Functions Name: 1 Definition of Logarithm: y = log x if and only if b = x b > 0, b 1, x > 0 How does Mr. Bean say log x? How does Mr. Kelly say log
More informationPolynomials. Eve Rawley, (EveR) Anne Gloag, (AnneG) Andrew Gloag, (AndrewG)
Polynomials Eve Rawley, (EveR) Anne Gloag, (AnneG) Andrew Gloag, (AndrewG) Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book,
More informationNewton s Cooling Model in Matlab and the Cooling Project!
Newton s Cooling Model in Matlab and the Cooling Project! James K. Peterson Department of Biological Sciences and Department of Mathematical Sciences Clemson University March 10, 2014 Outline Your Newton
More informationMAT137 - Week 8, lecture 1
MAT137 - Week 8, lecture 1 Reminder: Problem Set 3 is due this Thursday, November 1, at 11:59pm. Don t leave the submission process until the last minute! In today s lecture we ll talk about implicit differentiation,
More informationEdexcel AS and A Level Mathematics Year 1/AS - Pure Mathematics
Year Maths A Level Year - Tet Book Purchase In order to study A Level Maths students are epected to purchase from the school, at a reduced cost, the following tetbooks that will be used throughout their
More informationFinite Mathematics : A Business Approach
Finite Mathematics : A Business Approach Dr. Brian Travers and Prof. James Lampes Second Edition Cover Art by Stephanie Oxenford Additional Editing by John Gambino Contents What You Should Already Know
More information2.4 Log-Arithm-etic. A Practice Understanding Task
2.4 Log-Arithm-etic A Practice Understanding Task Abe and Mary are feeling good about their log rules and bragging about their mathematical prowess to all of their friends when this exchange occurs: CC
More informationOne sided tests. An example of a two sided alternative is what we ve been using for our two sample tests:
One sided tests So far all of our tests have been two sided. While this may be a bit easier to understand, this is often not the best way to do a hypothesis test. One simple thing that we can do to get
More informationA factor times a logarithm can be re-written as the argument of the logarithm raised to the power of that factor
In this section we will be working with Properties of Logarithms in an attempt to take equations with more than one logarithm and condense them down into just a single logarithm. Properties of Logarithms:
More informationCS173 Lecture B, November 3, 2015
CS173 Lecture B, November 3, 2015 Tandy Warnow November 3, 2015 CS 173, Lecture B November 3, 2015 Tandy Warnow Announcements Examlet 7 is a take-home exam, and is due November 10, 11:05 AM, in class.
More informationTo factor an expression means to write it as a product of factors instead of a sum of terms. The expression 3x
Factoring trinomials In general, we are factoring ax + bx + c where a, b, and c are real numbers. To factor an expression means to write it as a product of factors instead of a sum of terms. The expression
More informationSTEP 1: Ask Do I know the SLOPE of the line? (Notice how it s needed for both!) YES! NO! But, I have two NO! But, my line is
EQUATIONS OF LINES 1. Writing Equations of Lines There are many ways to define a line, but for today, let s think of a LINE as a collection of points such that the slope between any two of those points
More informationLecture 09 Combined Effect of Strain, Strain Rate and Temperature
Fundamentals of Materials Processing (Part- II) Prof. Shashank Shekhar and Prof. Anshu Gaur Department of Materials Science and Engineering Indian Institute of Technology, Kanpur Lecture 09 Combined Effect
More information29. GREATEST COMMON FACTOR
29. GREATEST COMMON FACTOR Don t ever forget what factoring is all about! greatest common factor a motivating example: cutting three boards of different lengths into same-length pieces solving the problem:
More informationLecture 5 - Logarithms, Slope of a Function, Derivatives
Lecture 5 - Logarithms, Slope of a Function, Derivatives 5. Logarithms Note the graph of e x This graph passes the horizontal line test, so f(x) = e x is one-to-one and therefore has an inverse function.
More information