Logarithms and Their Properties

Slides:



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

Logarithmic Equations Unknown Exponents Unknown Number Solving Logarithmic Equations Natural Logarithms.
7.2 Notes: Log basics. Exponential Functions:  Exponential functions have the variable located in the exponent spot of an equation/function.  EX: 2.
Properties of Logarithms
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”
MAC 1105 Section 4.3 Logarithmic Functions. The Inverse of a Exponential Function 
Logarithmic Functions and Models Lesson 5.4. A New Function Consider the exponential function y = 10 x Based on that function, declare a new function.
Exponential and Logarithmic Equations Lesson 5.6.
Section 3.4. Solving Exponential Equations Get your bases alike on each side of the equation If the variable is in the exponent set the exponents equal.
Objectives Write equivalent forms for exponential and logarithmic functions. Write, evaluate, and graph logarithmic functions.
7-3 Logarithmic Functions Understand how to write, evaluate, and graph logarithmic functions Success Criteria:  I can write logarithmic functions  I.
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”
Recall: These are equations of the form y=ab x-h +k, ones where the ‘x’ is in the exponent Recall: These are equations of the form y=ab x-h +k, ones where.
Properties of Logarithms By: Jennifer Garcia & Roslynn Martinez.
2. Condense: ½ ln4 + 2 (ln6-ln2)
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 =
Warm up. 3.4 Solving Exponential & Logarithmic Equations Standards 13, 14.
Solving Exponential and Logarithmic Equations Section 8.6.
Solving Exponential and Logarithmic Equations Section 6.6 beginning on page 334.
Unit 5: Modeling with Exponential & Logarithmic Functions Ms. C. Taylor.
Natural Logarithms.
Sec 4.1 Exponential Functions Objectives: To define exponential functions. To understand how to graph exponential functions.
Exponentials without Same Base and Change Base Rule.
Logarithms and Their Properties Lesson 4.1. Recall the Exponential Function General form  Given the exponent what is the resulting y-value? Now we look.
Logarithms 1 Converting from Logarithmic Form to Exponential Form and Back 2 Solving Logarithmic Equations & Inequalities 3 Practice Problems.
Unit 5: Logarithmic Functions Inverse of exponential functions. “log base 2 of 6” Ex 1: Domain: all real numbers Range: y > 0 “log base b of x” Domain:
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.
Chapter 5: Exponential and Logarithmic Functions 5.5: Properties and Laws of Logarithms Essential Question: What are the three properties that simplify.
Solving Logarithmic Equations
Lesson 3.4 Properties of Logarithms
Daily Warm-UP Quiz 1.Expand: ln x -5 y 2 2x 2. Condense: ½ ln4 + 2 (ln6-ln2) 3. Use properties of logs to solve for x: a. log 81 = x log3 b. log x 8/64.
Property of Logarithms If x > 0, y > 0, a > 0, and a ≠ 1, then x = y if and only if log a x = log a 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.
Logarithmic Properties Exponential Function y = b x Logarithmic Function x = b y y = log b x Exponential Form Logarithmic Form.
LOGARITHMIC AND EXPONENTIAL EQUATIONS LOGARITHMIC AND EXPONENTIAL EQUATIONS SECTION 4.6.
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.
Properties of Logarithms Pre-Calculus Teacher – Mrs.Volynskaya.
Algebra The Natural Base, e. Review Vocabulary Exponential Function–A function of the general form f(x) = ab x Growth Factor – b in the exponential.
10.2 Logarithms & Logarithmic Functions
Exponential and Logarithmic Function
6.1 - Logarithmic Functions
Solving Exponential and Logarithmic Equations
PROPERTIES OF LOGARITHMS
Logarithmic Functions
Logarithmic Functions and Their Graphs
Logarithms and Their Properties
Logarithmic Functions
Review of Logarithms.
LOGARITHMS AND THEIR PROPERTIES
Unit 8 [7-3 in text] Logarithmic Functions
Properties of Logarithms
Packet #15 Exponential and Logarithmic Equations
5.4 Logarithmic Functions and Models
Properties of Logarithms
Logarithmic Functions and Models
Deriving and Integrating Logarithms and Exponential Equations
Exponential and Logarithmic Equations
Logarithmic Functions and Their Graphs
Logarithmic Functions
Introduction to Logarithms
Solving Exponential & logarithmic Equations
5A.1 - Logarithmic Functions
Logarithmic Functions
Logarithmic Functions & Their Graphs
Solve for x: 1) xln2 = ln3 2) (x – 1)ln4 = 2
3.4 Exponential and Logarithmic Equations
6.1 - Logarithmic Functions
Warm-up: Solve for x: CW: Practice Log Quiz HW: QUIZ Review 3.1 – 3.4.
Logarithmic Functions
Presentation transcript:

Logarithms and Their Properties Lesson 5.1

Recall the Exponential Function General form Given the exponent what is the resulting y-value? Now we look at the inverse of this function Now we will ask, given the result, what exponent is needed to achieve it?

A New Function Consider the exponential function y = 10x Based on that function, declare a new function x = log10y You should be able to see that these are inverse functions In general The log of a number is an exponent

Note: if no base specified, default is base of 10 The Log Function Try These log39 = ? log232 = ? log 0.01 = ? Note: if no base specified, default is base of 10

Properties of Logarithms Note box on page 154 of text Most used properties

Natural Logarithms We have used base of 10 for logs Another commonly used base for logs is e e is an irrational number (as is ) e has other interesting properties Later to be discovered in calculus Use ln button on your calculator

Properties of the Natural Logarithm Recall that y = ln x  x = ey Note that ln 1 = 0 and ln e = 1 ln (ex) = x (for all x) e ln x = x (for x > 0) As with other based logarithms

Use Properties for Solving Exponential Equations Given Take log of both sides Use exponent property Solve for what was the exponent Note this is not the same as log 1.04 – log 3

Misconceptions log (a+b) NOT the same as log a + log b log (a * b) NOT same as (log a)(log b) log (a/b) NOT same as (log a)/(log b) log (1/a) NOT same as 1/(log a)

Assignment Lesson 5.1 Page 185 Exercises 1 – 51 odd