Aim: Logarithm Equations Course: Alg. 2 & Trig. Aim: How do we solve logarithm equations? Do Now:

Slides:

Advertisements

Similar presentations

Aim: How do we solve equations with fractions, negative numbers, or variables in the exponents? Do Now: Meteorologists use the formula D3 = 216T2 to describe.

Advertisements

Exponential functions Logarithmic functions

Copyright © 2009 Pearson Education, Inc. CHAPTER 5: Exponential and Logarithmic Functions 5.1 Inverse Functions 5.2 Exponential Functions and Graphs 5.3.

Properties of Logarithms

Table of Contents Solving Logarithmic Equations A logarithmic equation is an equation with an expression that contains the log of a variable expression.

Using the Properties of Logs. You already learned how to solve simple log equations. Now we are going a step or two farther. These equations are solved.

“Before Calculus”: Exponential and Logarithmic Functions

Exponential and Logarithmic Equations

7.6 – Solve Exponential and Log Equations

Objectives Solve exponential and logarithmic equations and equalities.

EQ: How do you use the properties of exponents and logarithms to solve equations?

11.3 – Exponential and Logarithmic Equations. CHANGE OF BASE FORMULA Ex: Rewrite log 5 15 using the change of base formula.

8.5 – Exponential and Logarithmic Equations. CHANGE OF BASE FORMULA where M, b, and c are positive numbers and b, c do not equal one. Ex: Rewrite log.

Warm-Up 4/30 Answer: $62, $60, Logarithmic Functions  The inverse of y = b x is _______  The function x = b y is called a___________.

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

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

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

Warmup Alg 2 27 Feb Warmup Alg 2 28 & 29 Feb 2012.

8.5 – Using Properties of Logarithms. Product Property:

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 8–4) Then/Now Key Concept: Product Property of Logarithms Example 1:Use the Product Property.

Solving Log Equations  We will be using all of the properties.  You will have to figure out which ones to use and when to use them.  You will have.

Solving Logarithmic Equations

Warm ups 1. Write the equation in exponential form.

Aim: Exponential Equations using Logs Course: Alg. 2 & Trig. Aim: How do we solve exponential equations using logarithms? Do Now:

Unit 5: Properties of Logarithms MEMORIZE THEM!!! Exponential Reasoning [1] [2] [3] [4] Cannot take logs of negative number [3b]

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

Unit 5: Logarithmic Functions

Properties of Logarithmic Functions Properties of Logarithmic Functions Objectives: Simplify and evaluate expressions involving logarithms Solve equations.

Aim: Log Products & Quotients Course: Alg. 2 & Trig. Aim: How do we use logarithms to find values of products and quotients? Do Now: Evaluate to prove.

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

Properties of Logarithms. Product property of logarithms For all positive numbers m, n, and b, where b  1, log b mn = log b m + log b n.

Solving One Step Equations Notes and Practice Problems.

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

Solving Logarithmic Equations

Section 5.5 Solving Exponential and Logarithmic Equations Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

Aim: Solving Rational Equations Course: Adv. Alg. & Trig. Aim: How do we solve rational equations? Do Now: Simplify:

Solve one step equations. You can add the same amount to both sides of an equation and the statement will remain true = = 9 x = y +

Warm Up Solve. 1. x + 5 = 9 2. x – 34 = 72 = x – 39 x = 4 x = 106

Holt McDougal Algebra Exponential and Logarithmic Equations and Inequalities Solve logarithmic equations. Objectives.

8.3 – Logarithmic Functions and Inverses. What is a logarithm? A logarithm is the power to which a number must be raised in order to get some other number.

6-2: Properties of Logarithms Unit 6: Exponents/Logarithms English Casbarro.

7.2 even answers 24) ) )$ ) $ ) Between 10 and 11 years 34) About 0.85 mg 40a) 40b) 40c)

Unit 5: Logarithmic Functions Inverse of exponential functions. “log base 2 of 6” Ex 1: Domain: all real numbers Range: y > 0 “log base b of x” Domain:

2.6.1 MATHPOWER TM 12, WESTERN EDITION 2.6 Chapter 2 Exponents and Logarithms.

Aim: Solving Quadratic Equation by Factoring Course: Adv. Alg. & Trig Aim: How to solve quadratic equations? Do Now: I III II Rectangular Box Rectangular.

Holt McDougal Algebra Exponential and Logarithmic Equations and Inequalities 4-5 Exponential and Logarithmic Equations and Inequalities Holt Algebra.

Splash Screen. Concept Product Property of Logarithms Example.

8.5 – Exponential and Logarithmic Equations

Ch. 8.5 Exponential and Logarithmic Equations

8.5 – Exponential and Logarithmic Equations

Logarithmic Functions

3.4 Quick Review Express In 56 in terms of ln 2 and ln 7.

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponents and Logarithms

Logarithmic and exponential equations

Section 5.5 Additional Popper 34: Choice A for #1 – 10

Logarithmic and Exponential Equations

8.3 – Logarithmic Functions and Inverses

Logarithmic and Exponential Equations

3.4 Exponential and Logarithmic Equations

Logarithmic Functions

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.

Section 5.5 Additional Popper 34: Choice A for #1 – 10

Logarithmic and exponential equations

Logarithmic Functions

Presentation transcript:

Aim: Logarithm Equations Course: Alg. 2 & Trig. Aim: How do we solve logarithm equations? Do Now:

Aim: Logarithm Equations Course: Alg. 2 & Trig. Properties of Logarithms For any positive numbers M, N, and b, b  1, Each of the following statements is true. log b MN = log b M + log b NProduct Property log b M/N = log b M – log b NQuotient Property log b M k = k log b MPower Property log (3 5) = log 3 + log 5 log (3 / 5) = log 3 – log 5 log 3 5 = 5 log 3 Note: log a (M + N) ≠ log a M + log a N Note: base must be the same

Aim: Logarithm Equations Course: Alg. 2 & Trig. Property of Equality for Log functions Solving Log Equations using Properties 1.If log A = log B, then A = B: Property of Equality for Log functions 2.Like regular equations use the inverse operation to simplify an equation Ex. log x - 1/3 log 8 = log 7 x = 14 log x - log 8 1/3 = log 7 Undo Power Law of Logarithms Undo Quotient Law of Logarithms 3. What you do to one side, do exactly to the other

Aim: Logarithm Equations Course: Alg. 2 & Trig. Solving Log Equations using Properties Ex. log 4 (x – 3) + log 4 (x + 3) = 2 log 4 [( x – 3)(x + 3)] = 2 Undo Product Law of Logarithms When only some terms are logarithmic, consolidate to one side in form log b = N and convert to exponential equation. Write in Exponential Form ( x – 3)(x + 3) = 4 2 Multiply x 2 – 9 = 16 Check: log 4 (5 – 3) + log 4 (5 + 3) = 2 log 4 (-5 – 3) + log 4 (-5 + 3) = 2 -8 Log 4 (-8) is undefined; +5 is only answer x =  5 x = 5

Aim: Logarithm Equations Course: Alg. 2 & Trig. Log Equation Problem log x + log(x – 3) = 1 log x(x – 3) = 1 Undo Product Law of Logarithms Write in Exponential Form x (x + 3) = 10 1 Multiply x 2 + 3x = 10 Log of negative number is undefined Put in Standard Quadratic Form x 2 + 3x – 10 = 0 x = -5x = 2 Solve for x Factor trinomial (x + 5)(x – 2) = 0

Aim: Logarithm Equations Course: Alg. 2 & Trig. Application Problem The pH of a substance is the concentration of hydrogen ions, [H + ], measured in moles of hydrogen per liter of substance. It is given by the formula Find the amount of hydrogen in a liter of acid rain that has a pH of = log 10 1 – log 10 [H + ] = [H + ] 4.2 = 0 – log 10 [H + ] 4.2 = – log 10 [H + ] – 4.2 = log 10 [H + ] log 10 1 = 0 or moles of hydrogen Always check your answer

Aim: Logarithm Equations Course: Alg. 2 & Trig. Model Problem x2 x + 2 x = 0