a) y = 3 x b) y = -3 x c) y = (1/2) x d) y = -(1/2) x.

Slides:



Advertisements
Similar presentations
1 ln(x) e x Approximating functions Elementary Functions.
Advertisements

Differentiation of the Exponential Function (e x ) and Natural Logarithms (lnx) Exponential function e x.
CSE 246: Computer Arithmetic Algorithms and Hardware Design Instructor: Prof. Chung-Kuan Cheng Fall 2006 Lecture 11 Cordic, Log, Square, Exponential Functions.
Representing Functions by Power Series. A power series is said to represent a function f with a domain equal to the interval I of convergence of the series.
Representing Functions by Power Series. A power series is said to represent a function f with a domain equal to the interval I of convergence of the series.
Exponential Functions Intro. to Logarithms Properties.
5.2 Logarithmic Functions & Their Graphs
Copyright © Cengage Learning. All rights reserved. 3 Exponential and Logarithmic Functions.
8.5 Natural Logarithms. Natural Logarithms Natural Logarithm: a natural log is a log with base e (the Euler Number) log e x or ln x.
Exponential FunctionsLogarithms Properties of Logarithms Natural Logarithms Solving Exponential Equations
Solving Exponential Equations Using Logarithms
3.3 Properties of Logarithms Change of Base. When solve for x and the base is not 10 or e. We have changed the base from b to 10. WE can change it to.
Properties of Logarithms Section 4.3 Properties of Logarithms
Exponential/ Logarithmic
Questions over 4.6 HW???. 4.7 (Green) Solve Exponential and Logarithmic Equations No School: Monday Logarithms Test: 1/21/10 (Thursday)
Lesson 3-8 Derivative of Natural Logs And Logarithmic Differentiation.
Objectives: 1.Be able to convert a logarithmic function into an exponential function. 2.Be able to convert an exponential function into a logarithmic function.
1 Logarithms Definition If y = a x then x = log a y For log 10 x use the log button. For log e x use the ln button.
1. Use a property of logarithms to evaluate log Use log 5 ≈ and log 6 ≈ to approximate the value of log Expand ln 7 3 2x 4.
Chapter 3.4 Properties of Log Functions Learning Target: Learning Target: I can find the inverses of exponential functions, common logarithms (base 10),
8-6 Ticket Out Use natural logarithms to solve e–6x = 3.1.
Aim: How do we solve exponential and logarithmic equations ? Do Now: Solve each equation: a. log 10 x 2 = 6 b. ln x = –3 Homework: Handout.
5.4 – Properties and Applications of Logarithims.
5-4 Exponential & Logarithmic Equations
Rules of Logs 1: A log with no base has a base of 10 Ex: log 100 = 2  log = 2  100 = 102 2: Domain of logs log (~)  ~ > 0.
8-5 Exponential & Logarithmic Equations Strategies and Practice.
Natural Logarithms.
Solving Logarithmic Equations TS: Making decisions after reflection and review. Obj: Be able to solve equations involving logarithms Warm-Up: Solve for.
5-4 Exponential & Logarithmic Equations Strategies and Practice.
Today in Precalculus Go over homework Notes: Common and Natural Logarithms Homework.
Bell Work Evaluate using the Properties of Exponents
Table of Contents Logarithm Properties - Product Rule The Product Rule for logarithms states that... read as “the log of the product is the sum of the.
$1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 Welcome.
How are you all doing? Any questions about anything?
Aim: Log Products & Quotients Course: Alg. 2 & Trig. Aim: How do we use logarithms to find values of products and quotients? Do Now: Evaluate to prove.
5.3 Properties of Logarithms
E/ Natural Log. e y = a x Many formulas in calculus are greatly simplified if we use a base a such that the slope of the tangent line at y = 1 is exactly.
Chapter 5: Exponential and Logarithmic Functions 5.5: Properties and Laws of Logarithms Essential Question: What are the three properties that simplify.
Log Equations Review OBJ: Review for Quest 2.
Today in Precalculus Go over homework Notes: Solving Log Equations Homework Quiz Friday, January 10.
Slide 9- 1 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Properties of Logs Objective: Be able to use the properties of logarithms to expand and condense expressions. TS: Make decisions after reflection and review.
 The logarithmic function log b (x) returns the number y such that b y = x.  For example, log 2 (8) = 3 because 2 3 = 8.  b is called the base of the.
Warm-Up 1) Use log 3 5 = and log 3 6 = to approximate log ) Condense 7 log log 4 x + 3 log 4 y.
9.5 BASE E AND NATURAL LOGS. NATURAL BASE EXPONENTIAL FUNCTION An exponential function with base e  e is the irrational number … *These are used.
4.7 (Green) Solve Exponential and Logarithmic Equations No School: Monday Logarithms Test: 1/21/10 (Thursday)
3.3 Logarithmic Functions and Their Graphs
Copyright © Cengage Learning. All rights reserved. Pre-Calculus Honors 3.4: Solving Exponential and Logarithmic Equations Chapter 3 Test: Tues 12/15 and.
$100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300.
3.4 Solving Exponential and Logarithmic Equations.
4.2 Logarithms. b is the base y is the exponent (can be all real numbers) b CANNOT = 1 b must always be greater than 0 X is the argument – must be > 0.
NATURAL LOGARITHMS LESSON 10 – 3 MATH III. THE NUMBER E e is a mathematical constant found throughout math and science. Bell curve distributions Self-supporting.
Warm Up WARM UP Evaluate the expression without using a calculator.
Ch. 3 – Exponential and Logarithmic Functions
Derivatives of Log Functions
SOLVING (expand and condense)
BACK SOLUTION:
Derivatives of Log Functions
Worksheet Key 1/2/2019 9:28 PM Solving Exp and Log Equations.
Exponential Functions Intro. to Logarithms Properties of Logarithms
Area of R = [(ln x) – (x-2)] dx
Properties of logarithms
Logarithms!.
All slides © Christine Crisp
Warm Up  .
5.6 - Solving Logarithmic and Exponential Equations
Section 5.5 Additional Popper 34: Choice A for #1 – 10
Exponential and Logarithmic Functions
Exponential and Logarithmic Functions
Property #1 – Product Property log a (cd) =
Presentation transcript:

a) y = 3 x b) y = -3 x c) y = (1/2) x d) y = -(1/2) x

a) y = lnx + 1 b) y = lnx – 1 c) y = ln(x + 1) d) y = ln(x – 1)

a) 64 b) 16 c) 4 2√2 d) 4

a) 3 3x b) 27 c) 9 d) 3

1010 a) x =1/3 b) x = -2 c) x =½ d) x =-3

10 a) x = ½ b) x = 1 c) x = ¼ d) no solution

1010 a) 2 b) ½ c) 3/2 d) 2/3

1010 a) 10 y = x b) 10 x = y c) x y = 10 d) y x = 10

10 a) log q = p b) log p = q c) ln q = p d) ln p = q

a) 10 b) between 1 and 2 c) between 2 and 3 d) between 3 and 4

1010 a) 100 b) 10 c) 3 d) 2

1010 a) e b) 1 c) 0 d) 10

10 a) 0 b) 13 c) 1 d) no solution

10 a) log (2x/y) b) log (x 2 /y) c) log x 2 /log y d) log (x 2 y)

10 a) 3(log x + log y) b) log 3x + log 3y c) log 3xy d) log 3x + log y

1010 a) 2 b) ½ c) log 8 34 d) 4

1010 a) Log 297 b) Log 900 c) Ln 100 d) 2

10 a) e b) 7 c) e 7 d) no solution

10 a) 1/3 b) 2 c) 2/3 d) no solution

10 a) x = 13/2 b) x = 14 c) x = 35/2 d) x = 11

1010 a) x = 5 b) x = -2 c) x = 5 and x = -2 d) x = 21

10 a) x = 8 b) x = 5 c) x = 3 d) x = 1

10 a) x > 3 b) x < 3 c) x > 6 d) x < 6

a) about b) about c) about d) about 55 10

a) 5 b) about 3.32 c) about 7.47 d) about 3.49