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

Slides:



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

8.4 Logarithms p. 486.
Name : ______________ ( ) Class : ________ Date :_________ Objectives: Unit 7: Logarithmic and Exponential Functions Graphs Solving Equations of the Form.
Pre-Calc Lesson 5-5 Logarithms
Logarithmic Functions Section 2. Objectives Change Exponential Expressions to Logarithmic Expressions and Logarithmic Expressions to Exponential Expressions.
ACT Class Opener: rig_1213_f026.htm rig_1213_f026.htm
Section 8.4 Logarithmic Functions Evaluate logarithmic functions Graph logarithmic functions.
1) log416 = 2 is the logarithmic form of 4░ = 16
Aim: What is the natural logarithms? Do Now: HW: p.338 # 8,16,20,26,30,38,42,48,50,52,56,58 Given f(x) = e x write the inverse function.
Logarithmic Functions
Lesson 5-5 Logarithms. Logarithmic functions The inverse of the exponential function.
Solving Exponential Equations…
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”
Section 3.3a!!!. First, remind me… What does the horizontal line test tell us??? More specifically, what does it tell us about the function This function.
Section 4.1 Logarithms and their Properties. Suppose you have $100 in an account paying 5% compounded annually. –Create an equation for the balance B.
Logarithmic Functions Section 8.4. WHAT YOU WILL LEARN: 1.How to evaluate logarithmic functions.
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.
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.
Section 3.2 Logarithmic Functions. The Logarithmic Function.
Sec 4.1 Exponential Functions Objectives: To define exponential functions. To understand how to graph exponential functions.
Section 9.2 Exponential Functions  Evaluating Rational & Irrational Exponents  Graphing Exponential Functions f(x) = a x  Equations with x and y Interchanged.
Section 11-4 Logarithmic Functions. Vocabulary Logarithm – y is called this in the function Logarithmic Function – The inverse of the exponential function.
8.3-4 – Logarithmic Functions. Logarithm Functions.
ACTIVITY 37 Logarithmic Functions (Section 5.2, pp )
4.4 Evaluate Logarithms and Graph Logarithmic Functions Part 2.
Logarithmic Functions & Their Graphs
PRE-AP PRE-CALCULUS CHAPTER 3, SECTION 3 LOGARITHMIC FUNCTIONS AND THEIR GRAPHS
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.
5.2 Logarithmic Functions & Their Graphs Goals— Recognize and evaluate logarithmic functions with base a Graph Logarithmic functions Recognize, evaluate,
Section 1.4 Logarithmic Functions. Find x for the following: How about now?
Section 5.4 Logarithmic Functions. LOGARITHIMS Since exponential functions are one-to-one, each has an inverse. These exponential functions are called.
Chapter 4 – Exponential and Logarithmic Functions Logarithmic Functions.
Section 6.5 – Properties of Logarithms. Write the following expressions as the sum or difference or both of logarithms.
MAT 1221 Survey of Calculus Section 4.5 Derivatives of Logarithmic Functions
Review Exponential + Logarithmic Functions Math Analysis.
Lesson 10.5Base e and Natural Logs (ln) Natural Base (e): Natural Base Exponential Function: ( inverse of ln ) Natural Logarithm (ln): ( inverse of e )
8.4 Logarithmic Functions
Introduction to Logarithms Chapter 8.4. Logarithmic Functions log b y = x if and only if b x = y.
3.3 Logarithmic Functions and Their Graphs
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.
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 Properties Exponential Function y = b x Logarithmic Function x = b y y = log b x Exponential Form Logarithmic Form.
Solving Logarithmic Equations I.. Relationship between Exponential and Logarithmic Equations. A) Logs and Exponentials are INVERSES of each other. 1) That.
LOGARITHMIC AND EXPONENTIAL EQUATIONS LOGARITHMIC AND EXPONENTIAL EQUATIONS SECTION 4.6.
Precalculus Section 5.5 Define and apply logarithms
LOGARITHMS. Find the inverse function for each of the functions below. 1.f(x) = 3x – f(x) = 2 x.
 Logarithmic Functions; Properties of Logarithms.
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.
Logarithmic Functions & Their Graphs Goals— Recognize and evaluate logarithmic functions with base a Graph Logarithmic functions Recognize, evaluate, and.
Section Logs as Inverse Exponentials. Lesson Objective: Students will: Redevelop the log function by reversing a table for an exponential function.
Logarithmic Functions
Logarithmic Functions and Their Graphs
Logarithmic Functions
Do Now: Determine the value of x in the expression.
Unit 8 [7-3 in text] Logarithmic Functions
5.4 Logarithmic Functions and Models
Warm up.
MAT 150 – Class #17 Topics: Graph and evaluate Logarithmic Functions
Logarithmic Functions and Their Graphs
Logarithms and Logarithmic Functions
Simplifying Logarithms
Simplifying Logarithms
Logarithmic Functions & Their Graphs
3.4 Exponential and Logarithmic Equations
6.3 Logarithms and Logarithmic Functions
Logarithmic Functions
Exponential and Logarithmic Functions
Presentation transcript:

MAC 1105 Section 4.3 Logarithmic Functions

The Inverse of a Exponential Function 

Logarithmic Functions 

Example 1: Write each exponential equation in logarithmic form.   Example 2: Write each logarithmic equation in exponential form.

Evaluating Logarithms 

Basic Properties of Logarithms 

Graphs of Logarithmic Functions 

Example 6: Graph the following graphs.  

Special Logs  Common Log  This a logarithm with base 10.  If no base is indicated, we assume base 10.  We can find the common log of any positive number on the calculator.  Natural Log  This a logarithm with base e.  This is denoted as ln  We can find the natural log of any positive number on the calculator as well.