Unit 9. Unit 9: Exponential and Logarithmic Functions and Applications.

Slides:

Advertisements

Similar presentations

Exponential Functions o Work on Exploration 1: Exponential Functions page 22 o Definition of Exponential Function o Graphs of Exponential Growth & Decay.

Advertisements

Unit 6. For x  0 and 0  a  1, y = log a x if and only if x = a y. The function given by f (x) = log a x is called the logarithmic function with base.

8-6 Compound Interest and Exponential Growth

Section 5.4 – Properties of Logarithms. Simplify:

Essential Question: What are some of the similarities and differences between natural and common logarithms.

Logarithmic Equations Unknown Exponents Unknown Number Solving Logarithmic Equations Natural Logarithms.

Exponential Functions Intro. to Logarithms Properties.

8.4 Logarithms p. 486.

The natural number e and solving base e exponential equations

Properties of Logarithms

CH. 8.6 Natural Logarithms. Write 2 ln 12 – ln 9 as a single natural logarithm. 2 ln 12 – ln 9 = ln 12 2 – ln 9Power Property = lnQuotient Property 12.

MAC 1105 Section 4.3 Logarithmic Functions. The Inverse of a Exponential Function 

Chapter 8 Review. Rewrite into logarithm form: 1. 2.

LOGS EQUAL THE The inverse of an exponential function is a logarithmic function. Logarithmic Function x = log a y read: “x equals log base a of y”

8-1 Exploring Exponent Models Objectives:  To identify exponential growth and decay.  To define the asymptote  To graph exponential functions  To find.

Copyright © 2010 Pearson Education, Inc. All rights reserved Sec

Indeterminate form indeterminate form of type Indeterminate form indeterminate form of type Sec 4.5: Indeterminate Forms And L’Hospital’s Rule.

Notes Over 8.4 Rewriting Logarithmic Equations Rewrite the equation in exponential form.

Transcendental Functions Chapter 6. For x  0 and 0  a  1, y = log a x if and only if x = a y. The function given by f (x) = log a x is called the logarithmic.

Differentiating exponential functions.

Bellwork If you have 120 m of fencing to make three side-by-side enclosures, what is the maximum area that you can enclose? 450 sq m.

Laws of Logarithms 5.6. Laws of Logarithms O If M and N are positive real numbers and b is a positive number such that b  1, then O 1. log b MN = log.

Xy -21/16 1/ xy -25/4 5/ xy -22/9 2/ xy /3 21/9 xy /2 xy

Copyright © Cengage Learning. All rights reserved. Logarithmic, Exponential, and Other Transcendental Functions.

Section 9.2 Exponential Functions  Evaluating Rational & Irrational Exponents  Graphing Exponential Functions f(x) = a x  Equations with x and y Interchanged.

Copyright © 2009 Pearson Education, Inc. CHAPTER 5: Exponential and Logarithmic Functions 5.1 Inverse Functions 5.2 Exponential Functions and Graphs 5.3.

Logarithms Definition Graphing. What’s a Log? the logarithm of a number to a given base is the power or exponent to which the base must be raised in order.

Logs Midterm Review Pre-Calculus. Topic 1: Be able to change logarithmic and exponential forms.

Lesson – Defining, Rewriting and Evaluating Rational Exponents

10.3: rational exponents April 27, Objectives 1.Define rational exponents 2.Simplify expressions that contain rational exponents 3.Estimate the.

NATURAL LOGARITHMS. The Constant: e e is a constant very similar to π. Π = … e = … Because it is a fixed number we can find e 2.

Pre-Calc Lesson 5-2 Growth and Decay: Rational Exponents Rational Exponents: ( Fractions as exponents) b 1/q = q b 1 so b p/q = q b p Simplify: /4.

Pre-Cal 3.1 Exponential Functions. -Transforming exponential graphs: -natural base e: = … -To solve an exponential equation: 1. Rewrite the powers.

Trash-ket Ball Chapter 7 Exponents and Logarithms.

Slide: LOGARITHMS. Slide: 2 ? ? The use of logarithms is a fast method of finding an unknown exponent. Section 7.4 BaseExponent 9 = 81 ? ? 3 = 27.

BELL RINGER Write, in paragraph form, everything you remember about logarithmic and exponential functions including how to convert, solve logarithmic equations,

By : Daniel Carter.  A logarithm is a number to a given base is the power or exponent to which the base must be raised in order to produce that number.

Properties of Logarithms

MATH III – Exponential and Logarithmic Functions Exponential Growth and Decay.

TODAY IN ALGEBRA 2.0…  REVIEW: HW #3 Exponential Growth and Decay  Learning Target 1: 7.4 You will evaluate logarithms.  Independent Practice.

8-2: Exponential Decay Day 2 Objective Ca Standard 12: Students know the laws of fractional exponents, understand exponential functions and use these functions.

4.3 Laws of Logarithms. 2 Laws of Logarithms  Just like the rules for exponents there are corresponding rules for logs that allow you to rewrite the.

Logarithmic Properties Exponential Function y = b x Logarithmic Function x = b y y = log b x Exponential Form Logarithmic Form.

INVERSE Logarithmic and Exponential Graphs and Graphing.

MGSE9-12.A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

Solving Logarithmic Equations I.. Relationship between Exponential and Logarithmic Equations. A) Logs and Exponentials are INVERSES of each other. 1) That.

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Evaluate natural exponential and natural logarithmic functions. Model exponential.

Goals:  Understand logarithms as the inverse of exponents  Convert between exponential and logarithmic forms  Evaluate logarithmic functions.

Review of Logarithms. Review of Inverse Functions Find the inverse function of f(x) = 3x – 4. Find the inverse function of f(x) = (x – 3) Steps.

Solving Exponential and Logarithmic Equations

Solving Logarithmic Equations

Solving Logarithmic Equations

Warmup Convert to radical form: 2. Convert to rational form:

Rational Exponents.

Properties of Logarithms

Express the equation {image} in exponential form

Bell Ringer (in Math Journal)

Section 5.3 – Properties of Logarithms

The behaviour of as x→∞ is called which of the following?

Solve for x: 1) xln2 = ln3 2) (x – 1)ln4 = 2

Inverse, Exponential and Logarithmic Functions

4.3 – Differentiation of Exponential and Logarithmic Functions

3.4 Exponential and Logarithmic Equations

Lesson 64 Using logarithms.

Logarithms Definition Graphing.

Indeterminate form Indeterminate form

Growth Factor (b) = 1 ± Growth Rate (r)

Section 5.6 – Properties of Logarithms

Presentation transcript:

Unit 9

Unit 9: Exponential and Logarithmic Functions and Applications

Rational Exponents

Unit 9: Exponential and Logarithmic Functions and Applications

Exponential Functions

Unit 9: Exponential and Logarithmic Functions and Applications

Logarithmic Functions

Logarithms on a Calculator

Logarithmic Functions

Examples

Unit 9: Exponential and Logarithmic Functions and Applications

Percent Growth and Decay

Periodic Interest

e and ln(x)

Rules for Exponents and Logarithms

Exponential Growth and Decay