Logarithmic Functions Mrs. White Algebra II. What are logarithms? The inverse of the exponential function!

Slides:



Advertisements
Similar presentations
Logarithms – making complex calculations easy
Advertisements

WARM - UP. SOLVING EXPONENTIAL & LOGARITHMIC FUNCTIONS SECTION 3.4.
WARM - UP. SOLVING EXPONENTIAL & LOGARITHMIC FUNCTIONS SECTION 3.4.
Daily Warm-Up Quiz 1.Describe two ways to graph the inverse of a logarithmic function. 2.Name at least three features of the graph of a logarithmic function.
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.
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.
Chapter 3.4 Properties of Log Functions Learning Target: Learning Target: I can find the inverses of exponential functions, common logarithms (base 10),
Section 10.1 The Algebra of Functions. Section 10.1 Exercise #1 Chapter 10.
MAC 1105 Section 4.3 Logarithmic Functions. The Inverse of a Exponential Function 
6. 3 Logarithmic Functions Objectives: Write equivalent forms for exponential and logarithmic equations. Use the definitions of exponential and logarithmic.
Objectives Write equivalent forms for exponential and logarithmic functions. Write, evaluate, and graph logarithmic functions.
Design: D Whitfield, Logarithms – making complex calculations easy John Napier John Wallis Jost Burgi Johann Bernoulli.
6.6 – Solving Exponential Equations Using Common Logarithms. Objective: TSW solve exponential equations and use the change of base formula.
Properties of Logarithms: Lesson 53. LESSON OBJECTIVE: 1)Simplify and evaluate expressions using the properties of Logarithms. 2)Solve logarithmic equations.
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.
Warm – Up Practice worksheet 3.1 Practice identifying and using the correct formula which is necessary to solve a problem Compound Interests and Annuities.
Unit 5: Modeling with Exponential & Logarithmic Functions Ms. C. Taylor.
Algebra II. If x varies directly as z and k represents the constant of proportionality, what is the equation that models this variation?
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?
3.9: Derivatives of Exponential and Logarithmic Functions.
ACTIVITY 37 Logarithmic Functions (Section 5.2, pp )
Do Now (7.4 Practice): Graph. Determine domain and range.
Section 9.3 Logarithmic Functions  Graphs of Logarithmic Functions Log 2 x  Equivalent Equations  Solving Certain Logarithmic Equations 9.31.
7.4 Logarithmic Functions Write equivalent forms for exponential and logarithmic equations. Use the definitions of exponential and logarithmic functions.
10.1/10.2 Logarithms and Functions
Do Now: 7.4 Review Evaluate the logarithm. Evaluate the logarithm. Simplify the expression. Simplify the expression. Find the inverse of the function.
Logarithm Basics. The logarithm base a of b is the exponent you put on a to get b: i.e. Logs give you exponents! Definition of Logarithm a > 0 and b >
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.
Evaluate Logarithms and Graph Logarithmic Functions Lesson 7.4 Part I Algebra II.
Holt McDougal Algebra Logarithmic Functions Write equivalent forms for exponential and logarithmic functions. Write, evaluate, and graph logarithmic.
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.
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.
Inverse Relations and Functions OBJ:  Find the inverse of a relation  Draw the graph of a function and its inverse  Determine whether the inverse of.
Algebra II H Problem of the Day Homework p eoo Sketch the graphs of the following functions. Use a separate graph for each function. Hint: To.
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 Mrs. King Pre-Calculus. What are logarithms? The inverse of the exponential function!
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.
MAT 1226 Calculus II Section 6.2* The Natural Logarithmic Function
6.5 Applications of Common Logarithms Objectives: Define and use the common logarithmic function to solve exponential and logarithmic equations. Evaluate.
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.
EXAMPLE FORMULA DEFINITION 1.
Logarithmic Functions
EXPONENTIAL & LOGARITHMIC GRAPHS
Logarithmic Functions
Ch. 8.5 Exponential and Logarithmic Equations
6. 3 Logarithmic Functions Objectives: Write equivalent forms for exponential and logarithmic equations. Use the definitions of exponential and logarithmic.
Logarithmic Functions and Their Graphs
Logarithmic and exponential relationships
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Do Now: Determine the value of x in the expression.
College Algebra Chapter 4 Exponential and Logarithmic Functions
3.9: Derivatives of Exponential and Logarithmic Functions, p. 172
Homework Questions?.
Derivatives of Exponential and Logarithmic Functions
3.9: Derivatives of Exponential and Logarithmic Functions.
Logarithms and Logarithmic Functions
Logarithmic Functions and Their Graphs
Simplifying Logarithms
Write each in exponential form.
Simplifying Logarithms
5A.1 - Logarithmic Functions
3.4 Exponential and Logarithmic Equations
Derivatives of Exponential and Logarithmic Functions
L8-3 Obj: Students will use definition of log
6.3 Logarithmic Functions
Warm Up  .
Presentation transcript:

Logarithmic Functions Mrs. White Algebra II

What are logarithms? The inverse of the exponential function!

Graph:

Definitions of Logarithms The logarithmic function is the function, where b is any number such that is equivalent to The function is read "log base b of x".

10 3 = 1000log = = 16log 2 16 = = 10,000log = = 9log 3 9 = = 16log 4 16 = = 0.01log = -2 log 4 64 = 34 3 = 64 log 3 27 = 33 3 = 27 log 36 6 = 1 / /2 = 6 log 12 1= = 1 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q log x y = zx z = y log a 5 = ba b = 5 log p q = rp r = q c = log a bb = a c pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt

10 3 = 1000log = = 16log 2 16 = = 10,000log = = 9log 3 9 = = 16log 4 16 = = 0.01log = -2 log 4 64 = 34 3 = 64 log 3 27 = 33 3 = 27 log 36 6 = 1 / /2 = 6 log 12 1= = 1 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q log x y = zx z = y log a 5 = ba b = 5 log p q = rp r = q c = log a bb = a c pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt

10 3 = 1000log = = 16log 2 16 = = 10,000log = = 9log 3 9 = = 16log 4 16 = = 0.01log = -2 log 4 64 = 34 3 = 64 log 3 27 = 33 3 = 27 log 36 6 = 1 / /2 = 6 log 12 1= = 1 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q log x y = zx z = y log a 5 = ba b = 5 log p q = rp r = q c = log a bb = a c pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt

10 3 = 1000log = = 16log 2 16 = = 10,000log = = 9log 3 9 = = 16log 4 16 = = 0.01log = -2 log 4 64 = 34 3 = 64 log 3 27 = 33 3 = 27 log 36 6 = 1 / /2 = 6 log 12 1= = 1 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q log x y = zx z = y log a 5 = ba b = 5 log p q = rp r = q c = log a bb = a c pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt

10 3 = 1000log = = 16log 2 16 = = 10,000log = = 9log 3 9 = = 16log 4 16 = = 0.01log = -2 log 4 64 = 34 3 = 64 log 3 27 = 33 3 = 27 log 36 6 = 1 / /2 = 6 log 12 1= = 1 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q log x y = zx z = y log a 5 = ba b = 5 log p q = rp r = q c = log a bb = a c pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt

Change of Base Formula

The Formula

Examples

Homework 9.3 Worksheet #3 Change of Base Formula

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2025 SlidePlayer.com. Inc. All rights reserved.