ALISON BOWLING LOGARITHMS. LOGARITHMS (BASE 10) 10 0 = 1log 10 1 = 0 10 1 = 10log 10 10 = 1 10 2 = 100log 10 100 = 2 10 3 = 1000log 10 1000 = 3 10 -1.

Slides:

Advertisements

Similar presentations

Unit 9. Unit 9: Exponential and Logarithmic Functions and Applications.

Advertisements

Section 5.4 – Properties of Logarithms. Simplify:

Logarithmic Equations Unknown Exponents Unknown Number Solving Logarithmic Equations Natural Logarithms.

Exponential Functions Intro. to Logarithms Properties.

8.4 Logarithms p. 486.

The natural number e and solving base e exponential equations

Functions and Logarithms

8.5 Natural Logarithms. Natural Logarithms Natural Logarithm: a natural log is a log with base e (the Euler Number) log e x or ln x.

Solving Exponential Equations Using Logarithms

3.3 Properties of Logarithms Change of Base. When solve for x and the base is not 10 or e. We have changed the base from b to 10. WE can change it to.

CH. 8.6 Natural Logarithms. Write 2 ln 12 – ln 9 as a single natural logarithm. 2 ln 12 – ln 9 = ln 12 2 – ln 9Power Property = lnQuotient Property 12.

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.

3.9 Derivatives of Exponential and Logarithmic Functions.

3.9 Derivatives of Exponential and Logarithmic Functions.

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.

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

Logarithmic and Exponential Equations

8.5 – Using Properties of Logarithms. Product Property:

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

8.3-4 – Logarithmic Functions. Logarithm Functions.

Natural Logarithms Section 5.6. Lehmann, Intermediate Algebra, 4ed Section 5.6Slide 2 Definition of Natural Logarithm Definition: Natural Logarithm A.

3.9 Derivatives of Exponential and Logarithmic Functions.

Table of Contents Logarithm Properties - Product Rule The Product Rule for logarithms states that... read as “the log of the product is the sum of the.

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.

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

( ) EXAMPLE 5 Use inverse properties Simplify the expression. a.

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

3.3 Properties of Logarithms Change of base formula log a x =or.

Properties of Logarithms

 The logarithmic function log b (x) returns the number y such that b y = x.  For example, log 2 (8) = 3 because 2 3 = 8.  b is called the base of the.

BELL RINGER Write, in paragraph form, everything you remember about logarithmic and exponential functions including how to convert, solve logarithmic equations,

Solving Logarithmic Equations

Lesson 10.5Base e and Natural Logs (ln) Natural Base (e): Natural Base Exponential Function: ( inverse of ln ) Natural Logarithm (ln): ( inverse of e )

3.3 Logarithmic Functions and Their Graphs

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

Definition if and only if y =log base a of x Important Idea Logarithmic Form Exponential Form.

Solving Equations Exponential Logarithmic Applications.

Table of Contents Logarithm Properties - Quotient Rule The Quotient Rule for logarithms states that... read as “the log of the quotient is the difference.

LOGARITHMIC AND EXPONENTIAL EQUATIONS LOGARITHMIC AND EXPONENTIAL EQUATIONS SECTION 4.6.

8.6 Natural Logarithms.

NATURAL LOGARITHMS LESSON 10 – 3 MATH III. THE NUMBER E e is a mathematical constant found throughout math and science. Bell curve distributions Self-supporting.

 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.

7.4 Logarithms p. 499 What you should learn: Goal1 Goal2 Evaluate logarithms Graph logarithmic functions 7.4 Evaluate Logarithms and Graph Logarithmic.

Solving Exponential and Logarithmic Equations

Logarithmic Functions and Their Graphs

Ch. 3 – Exponential and Logarithmic Functions

Logs on the Calculator and Solving Exponential Functions

Use properties of logarithms

Definition y=log base a of x if and only if.

Packet #15 Exponential and Logarithmic Equations

5.4 Logarithmic Functions and Models

Express the equation {image} in exponential form

Logarithms and Logarithmic Functions

Logarithmic and Exponential Equations

Exponential Functions Intro. to Logarithms Properties of Logarithms

Logarithmic and Exponential Equations

4.3 – Differentiation of Exponential and Logarithmic Functions

3.4 Exponential and Logarithmic Equations

6.3 Logarithms and Logarithmic Functions

Warm Up Solve for x:

4.5 Properties of Logarithms

4 minutes Warm-Up Write each expression as a single logarithm. Then simplify, if possible. 1) log6 6 + log6 30 – log6 5 2) log6 5x + 3(log6 x – log6.

Properties of logarithms

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

Logarithmic Functions and their Graphs

Presentation transcript:

ALISON BOWLING LOGARITHMS

LOGARITHMS (BASE 10) 10 0 = 1log 10 1 = = 10log = = 100log = = 1000log = =.1log 10.1 = =.01log = =.001log = =.0001log = -4 Note: Log x where X <= 0 is undefined

LOGARITHMS (BASE E) Euler’s number, e = …. e x : exponential function e is of eminent importance in mathematics (alongside  ) e 1 = ….ln (2.718) = 1 e 2 = 7.39ln (7.39 ) = 2 e -2 = 1/7.39 =.135ln (0.135) = -2 In general, if y = e x thenln (y) = x

PROPERTIES OF LOGARITHMS