6. 3 Logarithmic Functions Objectives: Write equivalent forms for exponential and logarithmic equations. Use the definitions of exponential and logarithmic.

Slides:

Advertisements

Similar presentations

EXPONENTIAL FUNCTIONS: DIFFERENTIATION AND INTEGRATION Section 5.4.

Advertisements

5.2 Logarithmic Functions & Their Graphs

Pre-Calc Lesson 5-5 Logarithms

Logarithmic Functions (Day 1)

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”

Lesson 5-5 Logarithms. Logarithmic functions The inverse of the exponential function.

Objectives & Vocabulary

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.

6. 3 Logarithmic Functions Objectives: Write equivalent forms for exponential and logarithmic equations. Use the definitions of exponential and logarithmic.

Logarithmic Functions

Solve each equation for x. 1. 3x – 12 = 45 x = x = 39.2 Algebra 3 Warm-Up 5.3.

Exponential Equations Like Bases. Warm Up  The following quadratic equation has exactly one solution for x. Find the value of k. Explore more than one.

 If m & n are positive AND m = n, then  Can solve exponential equation by taking logarithm of each side of equation  Only works with base 10.

6. 3 Logarithmic Functions Objectives: Write equivalent forms for exponential and logarithmic equations. Use the definitions of exponential and logarithmic.

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

6.6 The Natural Base, e Objectives: Evaluate natural exponential and

Do Now (7.4 Practice): Graph. Determine domain and range.

6.6 The Natural Base, e Objectives: Evaluate natural exponential and natural logarithmic functions.

Section 9.3 Logarithmic Functions  Graphs of Logarithmic Functions Log 2 x  Equivalent Equations  Solving Certain Logarithmic Equations 9.31.

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

Log Introduction  Video  **** find*****. 8.3 Lesson Logarithmic Functions.

SOLVING LOGARITHMIC EQUATIONS Objective: solve equations with a “log” in them using properties of logarithms How are log properties use to solve for unknown.

7.4 Logarithmic Functions Write equivalent forms for exponential and logarithmic equations. Use the definitions of exponential and logarithmic functions.

Notes Over 5.2 Rewriting Logarithmic Equations and Rewrite the equation in exponential form. are equivalent. Evaluate each logarithm.

Logarithms – An Introduction Check for Understanding – Prove basic properties of logarithms using properties of exponents and apply those properties.

Applications of Common Logarithms Objective: Define and use common logs to solve exponential and logarithmic equations; use the change of base formula.

Holt McDougal Algebra Logarithmic Functions Write equivalent forms for exponential and logarithmic functions. Write, evaluate, and graph logarithmic.

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.

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.

Objective: Students will be able to write equivalent forms for exponential and logarithmic functions, and can write, evaluate, and graph logarithmic functions.

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.

Logarithmic Functions Algebra 2 Unit 2: Exponential and Logarithmic Functions.

Focus: 1. Recognize and evaluate logarithmic functions. Use logarithmic functions to solve problems.

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.

Collins Type I What assumption(s) do you make about a population’s growth when you make predictions by using an exponential expression?

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

6.5 Applications of Common Logarithms Objectives: Define and use the common logarithmic function to solve exponential and logarithmic equations. Evaluate.

Logarithmic Functions

5.2 Logarithmic Functions & Their Graphs

Aim: What is the logarithms?

Logarithmic Functions

8.5 – Exponential and Logarithmic Equations

8-5 Exponential and Logarithmic Equations

Solving Exponential Equations

8.5 – Exponential and Logarithmic Equations

Logarithmic Functions and Graphs

Logarithmic Functions and Their Graphs

5.3 Logarithmic Functions & Graphs

Section 6.4 Properties of Logarithmic Functions Objectives:

Do Now: Determine the value of x in the expression.

Solving Exponential Equations

Chapter 5: Inverse, Exponential, and Logarithmic Functions

5.4 Logarithmic Functions and Models

Logarithmic Functions and Their Graphs

EXPONENTIAL FUNCTIONS: DIFFERENTIATION AND INTEGRATION

Introduction to Logarithms

Warm Up Which plan yields the most interest? Invest $100 Plan A: A 7.5% annual rate compounded monthly for 4 years Plan B: A 7.2% annual rate compounded.

Algebra Exponential Functions

Warm-Up Find the inverse of each function. f(x) = x + 10 g(x) = 3x

8.3 – Logarithmic Functions and Inverses

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

Aim: What is the logarithms?

Which plan yields the most interest. Invest $100 Plan A: A 7

Logarithmic Functions

Algebra 2 Warmup.

6.3 Logarithms and Logarithmic Functions

Goes along with 4.4 (GREEN book)

Presentation transcript:

6. 3 Logarithmic Functions Objectives: Write equivalent forms for exponential and logarithmic equations. Use the definitions of exponential and logarithmic functions to solve equations. Standard: 2.8.11.S. Analyze properties and relationships of functions.

Logarithms are used to find unknown exponents in exponential models. Logarithmic functions define many measurement scales in the sciences, including the pH, decibel, and Richter scales.

With logarithms, you can write an exponential equation in an equivalent logarithmic form.

Ex 1. a. Write in logarithmic form. ________________________ b. Write in exponential form. _______________________ c. Write 112 = 121 in logarithmic form. _________________________ d. Write log 6 36 = 2 in exponential form. _______________________ e. Write 7-2=1/49 in logarithmic form. __________________________ f. Write log 3 1/81= -4 in exponential form. _______________________ 2 = log11 121 62 = 36 Log7 (1/49) = -2 3-4 = 1/81

You can evaluate logarithms with a base of 10 by using the log key on a calculator. Ex 2. Solve each equation for x. Round your answer to the nearest thousandth. a). 10x= 1/109 b). x = log101/109 x = -2.037 c). 10x= 1.498 d). 10x= 7210 x = log10 1.498 x = log107210 x = .176 x = 3.858

The inverse of the exponential function y = 10x is x = 10y. To rewrite x = 10y in terms of y, use the equivalent logarithmic form, y = log 10 x.

Examine the tables & graphs below to see the inverse relationship between y=10x and y = log10x.

Range: all positive Real #s BeBelow summarizes the relationship between the domain and range of y = 10x and of y = log10 X. y = 10x Domain: all Real #s Range: all positive Real #s y = log10 X Domain: all positive real #s Range: all Real #s

The logarithmic function y = log b x with base b, or x = by, is the inverse of the exponential function y = bx, where b ≠ 1 and b > 0. One-to-one Property of Exponents If bx = by, then x = y.

Ex. 3 Find the value of v in each equation. B. 5 = logv 32 v = log125 5 v5 = 32 125v = 5 (53)v = 5 v5 = 25 53v = 51 v = 2 3v = 1 v = 1/3

d. v = log464 4v = 64 4v = 43 (same base) v = 3 c. 4 = log3 v 34 = v 81 = v

e. 2 = logv25 v2 = 25 v2=52 v = 5 f. 6 = log3v v = 36 v = 729 g. v = log10 1000 10v = 1000 10v = 103 v = 3 e. 2 = logv25 v2 = 25 v2=52 v = 5 h. 2 = log7V V = 72 V = 49 f. 6 = log3v v = 36 v = 729 I. 1 = log3v 31 = v 3 = v

Homework Integrated Algebra II- Section 6.3 Level A Honors Algebra II- Section 6.3 Level B Read article and write one paragraph on your thoughts as they relate to the exponential growth of money