Solving Logarithmic Equations

Slides:



Advertisements
Similar presentations
Exponential & Logarithmic Equations
Advertisements

15.4, 5 Solving Logarithmic Equations OBJ:  To solve a logarithmic equation.
Essential Question: What are some of the similarities and differences between natural and common logarithms.
Logarithmic Equations Unknown Exponents Unknown Number Solving Logarithmic Equations Natural Logarithms.
Warm-Up. One way to solve exponential equations is to use the property that if 2 powers w/ the same base are equal, then their exponents are equal. For.
Standardized Test Practice
WARM - UP. SOLVING EXPONENTIAL & LOGARITHMIC FUNCTIONS SECTION 3.4.
Exponential and Logarithmic Equations
7-5 Logarithmic & Exponential Equations
Aim: How do we solve exponential and logarithmic equations ? Do Now: Solve each equation: a. log 10 x 2 = 6 b. ln x = –3 Homework: Handout.
Section 3.4. Solving Exponential Equations Get your bases alike on each side of the equation If the variable is in the exponent set the exponents equal.
7.6 – Solve Exponential and Log Equations
Solving Review Semester 2. Notice the variable is in the exponent. That means we need to use logs to solve. Because an “e” is involved we must use ln.
Logarithmic and Exponential Equations
EQ: How do you use the properties of exponents and logarithms to solve equations?
Warm up. 3.4 Solving Exponential & Logarithmic Equations Standards 13, 14.
Solving Exponential and Logarithmic Equations Section 6.6 beginning on page 334.
Solving Logarithmic Equations. We need to solve log equations to find the y intercept. We’ll use the log properties to help us do that. Type 1:
Unit 5: Modeling with Exponential & Logarithmic Functions Ms. C. Taylor.
3.4 Exponential and Logarithmic Equations Properties of Exp. and Log Functions log a a x = x ln e x = x.
Exponentials without Same Base and Change Base Rule.
Solving Logarithmic Equations
Solve a logarithmic equation
EXAMPLE 4 Solve a logarithmic equation Solve log (4x – 7) = log (x + 5). 5 5 log (4x – 7) = log (x + 5) x – 7 = x x – 7 = 5 3x = 12 x = 4 Write.
Solving Quadratic Equations – Part 1 Methods for solving quadratic equations : 1. Taking the square root of both sides ( simple equations ) 2. Factoring.
5.5 Objectives Apply the base properties of logarithms. Use the change of base formula.
Aim: Exponential Equations using Logs Course: Alg. 2 & Trig. Aim: How do we solve exponential equations using logarithms? Do Now:
Logarithms 1 Converting from Logarithmic Form to Exponential Form and Back 2 Solving Logarithmic Equations & Inequalities 3 Practice Problems.
SOLVING LOGARITHMIC EQUATIONS Objective: solve equations with a “log” in them using properties of logarithms How are log properties use to solve for unknown.
5-5 Solving Quadratic Equations Objectives:  Solve quadratic equations.
2.1 – Linear and Quadratic Equations Linear Equations.
Common Logarithms - Definition Example – Solve Exponential Equations using Logs.
Solving Logarithmic Equations
Converting between log form and exponential form.
15.4, 5 Solving Logarithmic Equations OBJ:  To solve a logarithmic equation.
ACTIVITY 39 Exponential and Logarithmic (Section 5.4, pp ) Equations.
4.7 (Green) Solve Exponential and Logarithmic Equations No School: Monday Logarithms Test: 1/21/10 (Thursday)
Property of Logarithms If x > 0, y > 0, a > 0, and a ≠ 1, then x = y if and only if log a x = log a y.
Properties of Logarithms and Common Logarithms Sec 10.3 & 10.4 pg
Solving Quadratic Equations. Find the quadratic equation if the solutions are 3 and -2. x = 3 x = -2 Make them equal zero. x – 3 = 0x + 2 = 0 (x – 3)(x.
Solving Equations Exponential Logarithmic Applications.
3.4 – Solving Exponential and Logarithmic Equations Ch. 3 – Exponential and Logarithmic Functions.
Topic 10 : Exponential and Logarithmic Functions Solving 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.
LOGARITHMIC AND EXPONENTIAL EQUATIONS LOGARITHMIC AND EXPONENTIAL EQUATIONS SECTION 4.6.
3.4 Solving Exponential and Logarithmic Equations.
LOGARITHMIC AND EXPONENTIAL EQUATIONS Intro to logarithms and solving exponential equations.
LOGARITHMIC FUNCTIONS. LOG FUNCTIONS Exact Values Find the exact value of log 3 81 log 3 81 = x 3 x = 81 3 x = 3 4 x = 4 1.Set the equation equal to.
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.
Solving Exponential and Logarithmic Equations
Exponential Equations
8.6 Solving Exponential & Logarithmic Equations
Change of Base.
Properties of Logarithms
A quadratic equation is written in the Standard Form,
SECTION 9-3 : SOLVING QUADRATIC EQUATIONS
Mrs. Volynskaya Pre-Calculus Exponential & Logarithmic Equations
Exponential & Logarithmic Equations
Bell Ringer (in Math Journal)
Solving Quadratic Equations by Factoring
Solve for x: 1) xln2 = ln3 2) (x – 1)ln4 = 2
a + 2 = 6 What does this represent? 2 a
3.4 Exponential and Logarithmic Equations
Exponential & Logarithmic Equations
Exponential & Logarithmic Equations
Objective Solve radical equations.. Objective Solve radical equations.
Chapter 8 Section 6 Solving Exponential & Logarithmic Equations
Compound Interest If a principal P is invested at an interest rate r for a period of t years, then the amount A of the investment is given by A = P(1 +
8-6 Natural Logarithms.
Definition of logarithm
Presentation transcript:

Solving Logarithmic Equations PART ONE

Recall: If we have like bases then the exponents are equal. Use Quadratic Formula or Factor or P/Q. 0 = (x - 4)(x + 1)

YOU CANNOT DIVIDE 14 by 2 NOR CAN YOU CANCEL OUT THE LOGS!!! Divide by 3 first. Take the log of both sides so that we can use the PROPERTIES!!! log log Remember that log 2 is just a number so divided both sides by log 2. log 2 log 2 = 3.807

log log log 3 log 3 Move 4 and divide by 2. Let’s take a log of each side. log log Now that we’ve take the log of each side we can use are properties. log 3 log 3

ln ln Move 4. Because we have an “e” we use natural logs. Remember that the ln e is ONE!!!

Set each factor equal to zero and solve using natural logs. Use QF or factor Set each factor equal to zero and solve using natural logs.