Objectives: 1.Be able to convert a logarithmic function into an exponential function. 2.Be able to convert an exponential function into a logarithmic function.

Slides:

Advertisements

Similar presentations

I.1 ii.2 iii.3 iv.4 1+1=. i.1 ii.2 iii.3 iv.4 1+1=

Advertisements

I.1 ii.2 iii.3 iv.4 1+1=. i.1 ii.2 iii.3 iv.4 1+1=

Exponential Functions Intro. to Logarithms Properties.

8.4 Logarithms p. 486.

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

WARM - UP. SOLVING EXPONENTIAL & LOGARITHMIC FUNCTIONS SECTION 3.4.

WARM - UP. SOLVING EXPONENTIAL & LOGARITHMIC FUNCTIONS SECTION 3.4.

Questions over 4.6 HW???. 4.7 (Green) Solve Exponential and Logarithmic Equations No School: Monday Logarithms Test: 1/21/10 (Thursday)

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”

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.

Unit 11, Part 2: Logarithms, Day 2 Evaluating Logarithms

6.6 – Solving Exponential Equations Using Common Logarithms. Objective: TSW solve exponential equations and use the change of base formula.

LAWS OF LOGARITHMS SECTION 5.6. Why do we need the Laws? To condense and expand logarithms: To Simplify!

CONVERTING FROM ONE FORM TO ANOTHER EVALUATING PROPERTIES OF LOGS – EXPANDING AND CONDENSING Day 1:

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.

Solving Exponential and Logarithmic Equations Section 8.6.

Turn in your Quiz!!! Complete the following:. Section 11-5: Common Logarithms The questions are… What is a common log? How do I evaluate common logs?

Use mental math to evaluate.

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

3.4 Solving Exponential and Logarithmic Equations.

5.5Logarithms Objectives: I will be able to…  Rewrite equations between exponential and logarithmic forms  Evaluate logarithms  Solve logarithms.

Chapter 3 Exponential and Logarithmic Functions 1.

MAT 150 – Class #18. Objectives  Graph and evaluate logarithmic functions  Convert equations to logarithmic and exponential forms  Evaluate and apply.

Algebra II Honors January 5 th Students will complete daily warm-up problems. Students will be able to model exponential growth and decay. Students will.

Objectives: Be able to identify the properties of logarithms.

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.

5.3 Intro to Logarithms 2/27/2013. Definition of a Logarithmic Function For y > 0 and b > 0, b ≠ 1, log b y = x if and only if b x = y Note: Logarithmic.

Exponential and Logarithmic Functions.

Solving Exponential Equations. We can solve exponential equations using logarithms. By converting to a logarithm, we can move the variable from the exponent.

10.1/10.2 Logarithms and Functions

5.5Logarithms. Objectives: I will be able to…  Rewrite equations between exponential and logarithmic forms  Evaluate logarithms  Solve logarithms Vocabulary:

Graphing Log Functions Pre-Calculus. Graphing Logarithms Objectives:  Make connections between log functions and exponential functions  Construct a.

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

7.5 NOTES – APPLY PROPERTIES OF LOGS. Condensed formExpanded form Product Property Quotient Property Power Property.

Properties of Logarithms

4.5 Properties of Logarithms. Properties of Logarithms log log 6 3 log 4 32 – log 4 2 log 5 √5.

WARM - UP Evaluate: log 3 81 Solve for x: log5 (2x+3) = log5 (4x -3)

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

Chapter 3 Exponential and Logarithmic Functions

Converting between log form and exponential form.

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

Derivatives of Exponential and Logarithmic Functions

Chapter 5 Lesson 3 Exponential and Logarithmic Equations.

Solving Logarithmic Equations I.. Relationship between Exponential and Logarithmic Equations. A) Logs and Exponentials are INVERSES of each other. 1) That.

10.2 Logarithms and Logarithmic functions. Graphs of a Logarithmic function verse Exponential functions In RED y = 10 x.

Goals:  Understand logarithms as the inverse of exponents  Convert between exponential and logarithmic forms  Evaluate logarithmic functions.

SECTION 5-5A Part I: Exponentials base other than e.

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.

Algebra Exponential and Logarithmic Equations and Inequalities.

Ch. 8.5 Exponential and Logarithmic Equations

6.1 - Logarithmic Functions

Solving Logarithmic Equations

8-5 Exponential and Logarithmic Equations

Solving Logarithmic Equations

Logarithms and Logarithmic Functions

Logarithmic Functions

Simplifying Logarithms

Solving Exponential & logarithmic Equations

Simplifying Logarithms

Exponential and Logarithmic Equations

Rational Exponents and Nth Roots Objectives:

Properties of Logarithmic Functions

Objectives: Be able to define a rational function.

Evaluating Logarithms

Exponential Functions Intro. to Logarithms Properties of Logarithms

3.4 Exponential and Logarithmic Equations

4.5 Properties of Logarithms

6.1 - Logarithmic Functions

Warm-up: Solve for x: CW: Practice Log Quiz HW: QUIZ Review 3.1 – 3.4.

Presentation transcript:

Objectives: 1.Be able to convert a logarithmic function into an exponential function. 2.Be able to convert an exponential function into a logarithmic function. 3. Be able to convert a natural log (ln) into an exponential function. 4. Be able to evaluate log functions using the same base formula. Critical Vocabulary: Logarithmic Function, Natural Log, Exponential Function

I. Convert from a log into exponential a. Formula: y = log a x  x = a y b. Examples 1. log a 7 = 12 Solution: 7 = a log 4 x = 8 Solution: x = 4 8 II. Convert from an exponential into a log a. Formula: x = a y  log a x = y b. Examples 1. a 4 = 9 Solution: log a 9 = x = 12 Solution: log 5 12 = x

III. Natural Log into an exponential function a. Formula: y = ln x  x = e y b. Examples 1. ln 5 = x Solution: 5 = e x 2. ln x = 7 Solution: x = e 7 3. e x = 21 Solution: ln 21 = x

IV. Evaluating Logs a. Same base formula 1. Formula: If a u = a v, Then u = v 1. 3 x = 9 Solution: x = 2 2. log 2 4 = x Solution: x = 2 b. Examples Solution: x = -1 3 x = x = 4 2 x = x = 1/3 3. log 3 (1/3) = x 3 x = 3 -1

4. log 8 16 Solution: x = 4/3 5. log log 9 (1/3) Solution: x = -1/2 8 x = x = 2 4 3x = 4 4 x = 2 2 2x = 2 2x = 1Solution: x = 1/2 9 x = 1/3 3 2x = x = -1 IV. Evaluating Logs

7. log 1/ Solution: x = 8 (1/27) x = x = x = x = 2Solution: x = -2/3 IV. Evaluating Logs 8.

Homework: Page #3 – 27 odds, odds, 55, 57