STUDENTS WILL BE ABLE TO: CONVERT BETWEEN EXPONENT AND LOG FORMS SOLVE LOG EQUATIONS OF FORM LOG B Y=X FOR B, Y, AND X LOGARITHMIC FUNCTIONS.

Slides:

Advertisements

Similar presentations

Logarithmic Functions Section 3.2. Objectives Rewrite an exponential equation in logarithmic form. Rewrite a logarithmic equation in exponential form.

Advertisements

Logarithmic Functions

4.3 Logarithmic Functions and Graphs Do Now Find the inverse of f(x) = 4x^2 - 1.

5.2 Logarithmic Functions & Their Graphs

Logarithmic Functions Section 2. Objectives Change Exponential Expressions to Logarithmic Expressions and Logarithmic Expressions to Exponential Expressions.

Bell work Find the value to make the sentence true. NO CALCULATOR!!

Logarithmic Functions Section 3-2 Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 Definition: Logarithmic Function For x  0 and.

Definition of a Logarithmic Function For x > 0 and b > 0, b≠ 1, y = log b x is equivalent to b y = x The function f (x) = log b x is the logarithmic function.

SFM Productions Presents: Another saga in your continuing Pre-Calculus experience! 3.2Logarithmic Functions and their Graphs.

Exponential and Logarithmic Functions and Equations

Logarithmic Functions. Logarithm = Exponent Very simply, a logarithm is an exponent of ten that will produce the desired number. Y = Log 100 means what.

6.6 – Solving Exponential Equations Using Common Logarithms. Objective: TSW solve exponential equations and use the change of base formula.

Warm-up 1. Convert the following log & exponential equations 1. Convert the following log & exponential equations Log equationExponential Equation Log.

CONVERTING FROM ONE FORM TO ANOTHER EVALUATING PROPERTIES OF LOGS – EXPANDING AND CONDENSING Day 1:

BELL RINGER (IN MATH JOURNAL) What are the laws of exponents? 1. x m x n = 2. x m = x n 3. (xy) n = 4. (x) n = (y) 5. x –n = 6. x 0 = 7. (x m ) n =

Log a x y. Recognize and evaluate logarithmic functions with base a Graph logarithmic functions Recognize, evaluate, and graph natural logarithmic functions.

Logarithmic Functions Digital Lesson. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 Definition: Logarithmic Function For x  0.

Warm-up Solve: log3(x+3) + log32 = 2 log32(x+3) = 2 log3 2x + 6 = 2

Unit 5: Modeling with Exponential & Logarithmic Functions Ms. C. Taylor.

9.2 Exponential Functions. A function that can be expressed in the form f (x) = b x, b > 0 and b ≠ 1 is called an exponential function Domain =  Range.

Use mental math to evaluate.

Q Exponential functions f (x) = a x are one-to-one functions. Q (from section 3.7) This means they each have an inverse function. Q We denote the inverse.

Intro to Logarithms Goes along with 4.4 (GREEN book) Quiz: 1/12/10 Logs Test: 1/21/10.

5.5Logarithms Objectives: I will be able to…  Rewrite equations between exponential and logarithmic forms  Evaluate logarithms  Solve logarithms.

Do Now (7.4 Practice): Graph. Determine domain and range.

1. Evaluate the expressions: log 3 27log 2 ½ log Sketch the graph of f(x) = 4 x and tell the domain, range, intercept, asymptote, and end behavior.

Logarithms 2.5 Chapter 2 Exponents and Logarithms 2.5.1

PRE-AP PRE-CALCULUS CHAPTER 3, SECTION 3 LOGARITHMIC FUNCTIONS AND THEIR GRAPHS

Section 4.4 Logarithmic Functions. Definition:Definition: 2) A logarithm is merely a name for a certain exponent! 2) A logarithm is merely a name for.

STUDENTS WILL BE ABLE TO: CONVERT BETWEEN EXPONENT AND LOG FORMS SOLVE LOG EQUATIONS OF FORM LOG B Y=X FOR B, Y, AND X LOGARITHMIC FUNCTIONS.

The number e is ________________ It is also known as Euler’s number Irrational.

5.2 Logarithmic Functions & Their Graphs Goals— Recognize and evaluate logarithmic functions with base a Graph Logarithmic functions Recognize, evaluate,

Notes Over 5.2 Rewriting Logarithmic Equations and Rewrite the equation in exponential form. are equivalent. Evaluate each logarithm.

Section 5.4 Logarithmic Functions. LOGARITHIMS Since exponential functions are one-to-one, each has an inverse. These exponential functions are called.

3.4 Properties of Logarithmic Functions

5.4 Logarithmic Functions. Quiz What’s the domain of f(x) = log x?

Chapter 4 – Exponential and Logarithmic Functions Logarithmic Functions.

3.2 Logarithmic Functions 2015 Digital Lesson. 3.1 Warm-up Mr. Smith deposited $6,500 in an account that pays the account pays 4.5% interest, compounded.

The Logarithm as Inverse Exponential Function Recall: If y is a one to one function of x, to find the inverse function reverse the x’s and y’s and solve.

Graphing Log Functions Pre-Calculus. Graphing Logarithms Objectives:  Make connections between log functions and exponential functions  Construct a.

4.4 Logarithmic Functions Morgan From his TV show, what is Dexter’s last name?

February 13, 2012 At the end of today, you will be able to graph a logarithmic function. Warm-up: Describe the transformation for: f(x) = -3 x.

(a) (b) (c) (d) Warm Up: Show YOUR work!. Warm Up.

3.2 Logarithmic Functions. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 Intro Solving for an answer Solving for a baseSolving.

Find the inverse of each logarithm or exponential. Show work REVIEW Examples Finding Inverses of Logarithms and Exponentials.

5.0 Properties of Logarithms AB Review for Ch.5. Rules of Logarithms If M and N are positive real numbers and b is ≠ 1: The Product Rule: log b MN = log.

Exponential & Logarithmic functions. Exponential Functions y= a x ; 1 ≠ a > 0,that’s a is a positive fraction or a number greater than 1 Case(1): a >

3.2 Logarithmic Functions and Their Graphs We know that if a function passes the horizontal line test, then the inverse of the function is also a function.

Logarithmic Functions Section 3-2 Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 BIG PICTURE Logarithms are just another way to.

LEQ: How do you evaluate logarithms with a base b? Logarithms to Bases Other Than 10 Sec. 9-7.

Objectives: The student will be able to… 1)Graph exponential functions. 2)Solve exponential equations and inequalities.

3.2 Logarithmic Functions. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 Intro Solving for an answer Solving for a baseSolving.

LEQ: HOW DO YOU EVALUATE COMMON LOGARITHMS? Common Logarithms Sec. 9-5.

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.

3.2 – Logarithmic Functions and Their Graphs Ch. 3 – Exponential and Logarithmic Functions.

2.5.1 MATHPOWER TM 12, WESTERN EDITION 2.5 Chapter 2 Exponents and Logarithms.

BELL RINGER  1. How do you convert from a logarithm to an exponential?  2. What are the properties of logarithms that come from the laws of exponents?

Logarithmic Functions & Their Graphs Goals— Recognize and evaluate logarithmic functions with base a Graph Logarithmic functions Recognize, evaluate, and.

Logarithmic Functions

Logarithmic Functions

5.4 Logarithmic Functions and Models

Logarithmic Functions and Their Graphs

Simplifying Logarithms

Simplifying Logarithms

Properties of Logarithmic Functions

6.3 Logarithms and Logarithmic Functions

Logarithmic Functions

6.3 Logarithmic Functions

Presentation transcript:

STUDENTS WILL BE ABLE TO: CONVERT BETWEEN EXPONENT AND LOG FORMS SOLVE LOG EQUATIONS OF FORM LOG B Y=X FOR B, Y, AND X LOGARITHMIC FUNCTIONS

LOGARITHMS Read as “log base a of x”

LOGARITHMS ARE EXPONENTS!

CONVERTING BETWEEN LOG AND EXPONENTIAL FORM

WITHOUT A CALCULATOR, FIND THE FOLLOWING

COMMON LOGARITHMS

PROPERTIES OF LOGS

USING THE PROPERTIES OF LOGS

HOMEWORK Pg 195 # 3-6, 11-20, Difference Quotient Video Project due next class!!

GRAPHS OF LOGARITHMIC FUNCTIONS

Domain: (0, ∞) Range: (- ∞, ∞) x-intercept: (1, 0) y-int: none Increasing: (0, ∞) Vertical Asymptote: x=0 HA: none Continuous: Yes Reflection of the graph y = a x in the line y=x

STEPS TO GRAPHING LOG FUNCTIONS

TRANSFORMATIONS OF LOG FUNCTIONS xy xyxy Domain: Range: VA: x-int:

TRANSFORMATIONS OF LOG FUNCTIONS xy xyxy Domain: Range: VA: xy

TRANSFORMATIONS OF LOG FUNCTIONS Domain: Range: VA: x-int: xy xyxyxy

FIND THE DOMAIN 1.f(x) = log 7 (x-4) 2.g(x)= log (1-2x) 3.g(x)= log 8 x 2 How do you think we can find the domain? Remember, we can’t take the log of a negative number. Set the piece inside the log greater than or equal to zero, then solve!

CHANGE OF BASE FORMULA Any number you want!

THE NATURAL LOGARITHM

PROPERTIES OF NATURAL LOGS

USING THE PROPERTIES OF NATURAL LOGS

QUIZ THURSDAY 3.1 Exponential Functions and their graphs Evaluate exponential functions Graph exponential functions Properties of exp graphs Natural base Graph Evaluate Compound Interest Solve 1-to1 exp equations 3.2 Logarithmic Functions and their graphs Evaluate log functions Graph log functions Properties of log graphs Properties of logs Common Log Change of Base Natural Log Evaluate

HOMEWORK Pg 195 #35, 41, 43, 45-48, 50, 51(53-61 odd)