Exponentials and Logarithms

Slides:

Advertisements

Similar presentations

Exponential and Logarithmic Functions 5 Exponential Functions Logarithmic Functions Differentiation of Exponential Functions Differentiation of Logarithmic.

Advertisements

Name : ______________ ( ) Class : ________ Date :_________ Objectives: Unit 7: Logarithmic and Exponential Functions Graphs Solving Equations of the Form.

7.2The Natural Logarithmic and Exponential Function Math 6B Calculus II.

The exponential function occurs very frequently in mathematical models of nature and society.

Exponential and Logarithmic Equations Lesson 5.6.

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.

 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.

Solving Exponential and Logarithmic Equations Section 6.6 beginning on page 334.

Chapter Exponential and logarithmic equations.

Unit 5: Modeling with Exponential & Logarithmic Functions Ms. C. Taylor.

1.Every Person in your group needs a piece of paper, a pencil, graph paper, and a calculator. 2.Every Person in your group needs a letter, either T, R,

Derivatives of Exponential Functions Lesson 4.4. An Interesting Function Consider the function y = a x Let a = 2 Graph the function and it's derivative.

Copyright © Cengage Learning. All rights reserved. Logarithmic, Exponential, and Other Transcendental Functions.

Solving Logarithmic Equations To solve today's equations, we are going to rewrite them in exponential form and use the methods learned in the last unit.

LOGARITHMIC EQUATIONS. CREATE A LOGARITHMIC EQUATION  Create a logarithmic function of the form  f(x) = log b (x-h) + k.

Power Functions, Comparing to Exponential and Log Functions Lesson 11.6.

Logarithms 1 Converting from Logarithmic Form to Exponential Form and Back 2 Solving Logarithmic Equations & Inequalities 3 Practice Problems.

Derivatives of Logarithmic Functions Objective: Obtain derivative formulas for logs.

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.

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.

Solve by Factoring Zero Product Property.

Derivative of Exponential Function and Logarithms I Logarithms, still.

Solving Logarithmic Equations

12.8 Exponential and Logarithmic Equations and Problem Solving Math, Statistics & Physics 1.

Chapter 5 Lesson 3 Exponential and Logarithmic Equations.

Homework Questions. LOGS Warm-up Evaluating Logs.

LOGARITHMIC AND EXPONENTIAL EQUATIONS LOGARITHMIC AND EXPONENTIAL EQUATIONS SECTION 4.6.

Copyright © 2010 Pearson Education, Inc. All rights reserved Sec

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

Derivatives of Logarithmic Functions

Ch. 8.5 Exponential and Logarithmic Equations

Logarithmic Functions and Their Graphs

Packet #15 Exponential and Logarithmic Equations

5.4 Logarithmic Functions and Models

Exponential and Logarithmic Equations

5.6 Solving Exponential and Logarithmic Equations

Graphing Inequalities

Transformations L.O. All pupils can recall how changes in equations transform graphs of functions All pupils can confidently solve all the homework questions.

Derivatives of Exponential Functions

Solving Exponential & logarithmic Equations

Homework Questions.

Exponential and Logarithmic Equations

Further Recap of Topics

Optimisation L.O. All pupils understand how quadratics can model real life situations All pupils recognize how parts of the graph relate to the real life.

Simultaneous Equations

Solve for x: log3x– log3(x2 – 8) = log38x

Homework Questions.

All pupils can read off the base trigonometric graphs

Evaluating Logarithms

Composite Functions L.O.

Inverse, Exponential and Logarithmic Functions

Power Functions, Comparing to Exponential and Log Functions

3.4 Exponential and Logarithmic Equations

All pupils know what polynomials are

Indices and Powers L.O. All pupils can describe the different types of numbers All pupils can write natural numbers in index form and the other way around.

Product Rule L.O. All pupils can solve basic differentiation questions

Exam Style Questions Practice

All pupils can use circle theorems to solve a variety of questions

How does substitution help link equations and their graphs?

Logarithms – Changing the Base

All pupils can write exponentials as logarithms

The Quadratic Formula L.O.

All pupils can solve equations involving logs

Function Notation L.O. All pupils can understand function notation

Unit 5 – Section 1 “Solving Logarithms/Exponentials with Common Bases”

All pupils can manipulate geometric sequences

Presentation transcript:

Exponentials and Logarithms All pupils can convert between logarithmic and exponential forms Most pupils can derive the logarithmic laws All pupils can use logarithms to solve problems

Starter: Convert each of these exponential questions into logarithms in order to make them easier to solve Ext. How do the graphs of exponentials and the graphs of logarithms differ?

Exponentials and Logarithms All pupils can convert between logarithmic and exponential forms Most pupils can derive the logarithmic laws All pupils can use logarithms to solve problems

Page 251, Exercise 5E, questions on the right hand side Main 1: Page 251, Exercise 5E, questions on the right hand side

Write the laws of indices. Main 1: Write the laws of indices. Use the laws of indices to derive the laws of logarithms.

Main 1:

Exponentials and Logarithms All pupils can convert between logarithmic and exponential forms Most pupils can derive the logarithmic laws All pupils can use logarithms to solve problems

Look at the examples on page 252 and at the top of 253 Main 2: Look at the examples on page 252 and at the top of 253

Main 2: Exercise 5F

Exponentials and Logarithms All pupils can convert between logarithmic and exponential forms Most pupils can derive the logarithmic laws All pupils can use logarithms to solve problems

Wipeboards

Exponentials and Logarithms All pupils can convert between logarithmic and exponential forms Most pupils can derive the logarithmic laws All pupils can use logarithms to solve problems