LOGARITHMIC FUNCTIONS. Exponentiation: The third power of some number ‘b’ is the product of 3 factors of ‘b’. More generally, raising ‘b’ to the n-th.

Slides:

Advertisements

Similar presentations

Logarithms ISP 121.

Advertisements

Logarithmic Functions & Their Graphs

5.2 Logarithmic Functions & Their Graphs

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

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.

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

Objectives Write equivalent forms for exponential and logarithmic functions. Write, evaluate, and graph logarithmic functions.

Logarithmic Functions y = log a x, is read “the logarithm, base a, of x,” or “log, base a, of x,” means “the exponent to which we raise a to get x.”

Objectives Solve exponential and logarithmic equations and equalities.

Chapter 4.3 Logarithms. The previous section dealt with exponential function of the form y = a x for all positive values of a, where a ≠1.

Logarithmic Functions

Logarithmic Functions & Graphs, Lesson 3.2, page 388 Objective: To graph logarithmic functions, to convert between exponential and logarithmic equations,

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.

Slide Copyright © 2012 Pearson Education, Inc.

Sec 4.1 Exponential Functions Objectives: To define exponential functions. To understand how to graph exponential functions.

6.4 – Solving Logarithmic Equations and Inequalities Objective: TSW solve logarithmic equations and inequalities.

8.3-4 – Logarithmic Functions. Logarithm Functions.

LOGARITHMIC EQUATIONS. CREATE A LOGARITHMIC EQUATION  Create a logarithmic function of the form  f(x) = log b (x-h) + k.

LOGARITHMIC FUNCTIONS By C. SURESH, Mentor in Mathematics, APIIIT-Nuzvid,Krishna(Dt.), A.P., India.

Holt McDougal Algebra 2 Logarithmic Functions Holt Algebra 2Holt McDougal Algebra 2 How do we write equivalent forms for exponential and logarithmic functions?

Exponential and Logarithmic Functions Logarithms Exponential and Logarithmic Functions Objectives Switch between exponential and logarithmic form.

Logarithm Basics. The logarithm base a of b is the exponent you put on a to get b: i.e. Logs give you exponents! Definition of Logarithm a > 0 and b >

Common Logarithms - Definition Example – Solve Exponential Equations using Logs.

Converting between log form and exponential form.

12.8 Exponential and Logarithmic Equations and Problem Solving Math, Statistics & Physics 1.

Math 1304 Calculus I 1.6 Inverse Functions. 1.6 Inverse functions Definition: A function f is said to be one-to- one if f(x) = f(y) implies x = y. It.

Holt McDougal Algebra Exponential and Logarithmic Equations and Inequalities Solve logarithmic equations. Objectives.

8.4 Logarithmic Functions

Exponents – Logarithms xy -31/8 -2¼ ½ xy 1/8-3 ¼-2 ½ The function on the right is the inverse of the function on the left.

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

Exponential and log graphs Logarithms Identify all the graphs in the diagrams below. (2,16) (0,1) 0 y x  (3,125) 0 y x (0,1)  0 y 1 (4,16) x  0 y.

Definition if and only if y =log base a of x Important Idea Logarithmic Form Exponential Form.

Holt McDougal Algebra Exponential and Logarithmic Equations and Inequalities 4-5 Exponential and Logarithmic Equations and Inequalities Holt Algebra.

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

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

Logarithmic Functions

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Calculus I Hughes-Hallett

4.6 Type 2 Exponential Equations

Linear Equations in One Variable

Logarithmic Functions and Their Graphs

Logarithmic Functions

Copyright © 2006 Pearson Education, Inc

Definition y=log base a of x if and only if.

Exponential & Logarithmic Functions

Bellwork Find the value of x in each exponential equation.

Suggested Practice on Moodle Worksheet: Logarithms Problems

Unit 8 [7-3 in text] Logarithmic Functions

Packet #15 Exponential and Logarithmic Equations

5.4 Logarithmic Functions and Models

Lial/Hungerford/Holcomb/Mullins: Mathematics with Applications 11e Finite Mathematics with Applications 11e Copyright ©2015 Pearson Education, Inc. All.

Question Suppose exists, find the limit: (1) (2) Sol. (1) (2)

Pre- Calculus Lesson 1.1 begin Chapter 1: Functions.

Rational Expressions and Functions

Copyright © Cengage Learning. All rights reserved.

Logarithmic and Exponential Equations

Graphs of Logarithmic Functions and their Features

Objectives Write equivalent forms for exponential and logarithmic functions. Write, evaluate, and graph logarithmic functions.

Exponential and Logarithmic Forms

Logarithmic and Exponential Equations

Exponential and Logarithmic Functions

The Exponential Function and Logarithms

Exponential and Logarithmic Functions

Chapter 5: Exponential and Logarithmic Functions

Exponential and Logarithmic Functions

Goes along with 4.4 (GREEN book)

6-8 Roots and Zeros Given a polynomial function f(x), the following are all equivalent: c is a zero of the polynomial function f(x). x – c is a factor.

3.2 Graphing Exponential Functions

Matrix Algebra THE INVERSE OF A MATRIX © 2012 Pearson Education, Inc.

Presentation transcript:

LOGARITHMIC FUNCTIONS

Exponentiation: The third power of some number ‘b’ is the product of 3 factors of ‘b’. More generally, raising ‘b’ to the n-th power (n is a natural number) is done by multiplying n factors. Definition: If b≠1 and ‘y’ are any two positive real numbers, then there exists a unique real number ‘x’ satisfying the equation b x = y. This x is said to be the logarithm of y to the base b and is written as Log b y = x The idea of logarithms is to reverse the operation of exponentiation.

Thus log 3 9 = 2 since 3 2 = 9 log = 3 since 6 3 = 216 log = -2 since = 0.01 Similarly x 0 = 1 implies that log x 1 = 0 Notes: 1.Since the exponential function value can never be zero, we can say that logarithm of zero is undefined. 2. Similarly, logarithmic function is not defined for negative values.

Types of logarithms: Logarithms to base 10 are called common logarithms. Logarithms to base 2 are called binary logarithms. Logarithms to base ‘e’ are called natural logarithms. Identities:

Sol: Given that

FunctionDomainRange exex R (0, ∞ ) log e x (0, ∞ ) R y = log e x y = e x y = x x y (0, 1) (1, 0) Graph: