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

Slides:

Advertisements

Similar presentations

TH EDITION LIAL HORNSBY SCHNEIDER COLLEGE ALGEBRA.

Advertisements

Graphs of Exponential and Logarithmic Functions

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

Properties of Logarithms

Solving Exponential Equations. One-to-One Properties.

Logarithmic Functions

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

Logarithmic Functions & Their Graphs

Logarithmic Functions

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

Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

SECTION 4.4 LOGARITHMIC FUNCTIONS LOGARITHMIC FUNCTIONS.

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

Exponential & Logarithmic Functions

4.2 Logarithmic Functions

1) log416 = 2 is the logarithmic form of 4░ = 16

Sullivan PreCalculus Section 4.4 Logarithmic Functions Objectives of this Section Change Exponential Expressions to Logarithmic Expressions and Visa Versa.

5.4 Exponential and Logarithmic Equations Essential Questions: How do we solve exponential and logarithmic equations?

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

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

Exponential and Logarithmic Functions and Equations

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 and Exponential Equations

Logarithmic Functions. y = log a x if and only if x = a y The logarithmic function to the base a, where a > 0 and a  1 is defined: exponential form logarithmic.

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

Lesson 5-6: Logarithms and Logarithmic Functions

Algebra II w/trig. A logarithm is another way to write an exponential. A log is the inverse of an exponential. Definition of Log function: The logarithmic.

Exponential Functions Section 1. Exponential Function f(x) = a x, a > 0, a ≠ 1 The base is a constant and the exponent is a variable, unlike a power function.

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

Sullivan Algebra and Trigonometry: Section 5.3 Exponential Functions Objectives of this Section Evaluate Exponential Functions Graph Exponential Functions.

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.

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

6.3 Logarithmic Functions. Change exponential expression into an equivalent logarithmic expression. Change logarithmic expression into an equivalent.

10.2 Logarithms and Logarithmic Functions Objectives: 1.Evaluate logarithmic expressions. 2.Solve logarithmic equations and inequalities.

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

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.

Properties of Logarithms Change of Base Formula:.

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.

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

Section 5.5 Solving Exponential and Logarithmic Equations Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

Math 71B 9.3 – Logarithmic Functions 1. One-to-one functions have inverses. Let’s define the inverse of the exponential function. 2.

Algebra 2 Notes May 4,  Graph the following equation:  What equation is that log function an inverse of? ◦ Step 1: Use a table to graph the exponential.

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

Logarithmic Functions Logarithms Logarithmic Equations Logarithmic Functions Properties of Logarithms.

Graphing Exponential and Logarithmic Functions. Objective I can graph exponential functions using a graphing utility and identify asymptotes, intercepts,

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.

The Logarithmic Functions and Their Graphs Section 3.2.

Warm Up Evaluate the following. 1. f(x) = 2 x when x = f(x) = log x when x = f(x) = 3.78 x when x = f(x) = ln x when x =

Copyright © 2011 Pearson Education, Inc. Logarithmic Functions and Their Applications Section 4.2 Exponential and Logarithmic Functions.

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

Sullivan Algebra and Trigonometry: Section 6.4 Logarithmic Functions

10.2 Logarithms & Logarithmic Functions

Logarithmic Functions and Their Graphs

5.3 Logarithmic Functions & Graphs

Sullivan Algebra and Trigonometry: Section 6.3 Exponential Functions

Sullivan Algebra and Trigonometry: Section 6.3

Lesson 9 – 3 Logarithmic Functions

5.4 Logarithmic Functions and Models

Logarithmic Functions and Their Graphs

6.3 Logarithmic Functions

Section 5.2 – Logarithmic Functions

Logarithmic and Exponential Equations

6.3 Logarithms and Logarithmic Functions

Logarithmic Functions

4.3 Logarithmic Functions

EXPONENTIAL FUNCTION where (base) b > 0 and b For 0 < b < 1,

Sullivan Algebra and Trigonometry: Section 6.2

4.3 Logarithmic Functions

Logarithmic Functions

Presentation transcript:

Section 5.4 Logarithmic Functions

LOGARITHIMS Since exponential functions are one-to-one, each has an inverse. These exponential functions are called logarithms.

LOGARITHMIC FUNCTIONS The logarithmic function to the base a, where a > 0 and a ≠ 1, is denoted by y = log a x (read as “y is the logarithm to the base a of x”) and is defined by y = log a x if and only if x = a y The domain of the logarithmic function y = log a x is x > 0.

EXPONENTIAL AND LOGARITHMIC FORMS The exponential form of y = log a x is a y = x. The logarithmic form of a y = x is y = log a x.

GRAPHING LOGARITHMIC FUNCTIONS To quickly graph the logarithmic function y = log a x plot points for x = 1/a, 1, and a. xy 1/a−1−1 10 a1

PROPERTIES OF f (x) = log a x Domain:(0, ∞) Range:(−∞, ∞) The x-intercept of the graph is 1. There is no y- intercept. Vertical Asymptote: x = 0 Increasing if a > 1 Decreasing if 0 < a < 1

DOMAIN OF A LOGARITHMIC FUNCTIONS Since the logarithm of a negative number and the logarithm of zero cannot be taken, the argument of a logarithmic function must always be positive. That is, if Z is an algebraic expression in x, the domain of f (x) = log b Z is the set of numbers such that Z > 0.

COMMON AND NATURAL LOGARITHMS Logarithms with a base of 10 are called common logarithms. We denote this by log x. That is, log x = log 10 x. Logarithms with a base of e are called natural logarithms. We denote this by ln x. That is, ln x = log e x.

LOGARITHMIC EQUATIONS Equations that contain logarithms are called logarithmic equation. Some logarithmic equations can be solved by converting them to exponential form. However, when solving logarithmic equations, you must always check your solutions.