More Exponential and Logarithmic Equations We’re right in with more practice problems in Sec. 3.5b.

Slides:

Advertisements

Similar presentations

( ) EXAMPLE 3 Solve ax2 + bx + c = 0 when a = 1

Advertisements

Exponential and Logarithmic Equations Section 3.4.

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

EXAMPLE 1 Solve a quadratic equation having two solutions Solve x 2 – 2x = 3 by graphing. STEP 1 Write the equation in standard form. Write original equation.

EXAMPLE 1 Solve a simple absolute value equation Solve |x – 5| = 7. Graph the solution. SOLUTION | x – 5 | = 7 x – 5 = – 7 or x – 5 = 7 x = 5 – 7 or x.

Write decimal as percent. Divide each side by 136. Substitute 51 for a and 136 for b. Write percent equation. Find a percent using the percent equation.

Standardized Test Practice

Standardized Test Practice

Lesson 13.4 Solving Radical Equations. Squaring Both Sides of an Equation If a = b, then a 2 = b 2 Squaring both sides of an equation often introduces.

Solve an equation with an extraneous solution

5.4 Exponential and Logarithmic Equations Essential Questions: How do we solve exponential and logarithmic equations?

Exponential and Logarithmic Equations

7-5 Logarithmic & Exponential Equations

7.6 – Solve Exponential and Log Equations

Solving Equations with Logs Day 2. Solving equations with only one logarithm in it: If it is not base 10 and you can’t use your calculator, then the only.

Remember that exponential functions and logarithmic functions are inverses of each other. We will use this property to solve problems.

8 – 6 Solving Exponential and Logarithmic Equations Day2 Objective: CA. 11.1: Students understand the inverse relationship between exponents and logarithms.

Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.

Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.

Standardized Test Practice

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

4.4 Solving Exponential and Logarithmic Equations.

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.

Solving Exponential and Logarithmic Equations Section 8.6.

Solve an equation with an extraneous solution

( ) EXAMPLE 3 Standardized Test Practice SOLUTION 5 x = – 9 – 9

EXAMPLE 2 Rationalize denominators of fractions Simplify

3.6 Solving Quadratic Equations

Solving Rational Equations On to Section 2.8a. Solving Rational Equations Rational Equation – an equation involving rational expressions or fractions…can.

Solving Exponential and Logarithmic Equations There are lots of them in Sec. 3.5a.

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 Absolute Value Equations and Inequalities.

Solving Systems of Equations: The Elimination Method Solving Systems of Equations: The Elimination Method Solving Systems of Equations: The Elimination.

Logarithmic Functions Recall that for a > 0, the exponential function f(x) = a x is one-to-one. This means that the inverse function exists, and we call.

EXAMPLE 1 Solve by equating exponents Rewrite 4 and as powers with base Solve 4 = x 1 2 x – 3 (2 ) = (2 ) 2 x – 3x – 1– 1 2 = 2 2 x– x + 3 2x =

Lesson 4 Contents 11-3 Solving Quadratic Equations by Using the Quadratic Formula Objectives 1. Solve quadratic equations by using the Quadratic Formula.

Solving Equations That Lead to Quadratic Equations There are several methods one can use to solve a quadratic equation. Sometimes we are called upon to.

Solving Logarithmic Equations Tuesday, February 9, 2016.

1 7.5 Solving Radical Equations. 2 What is a radical equation? A radical equation is an equation that has a variable under a radical or that has a variable.

x + 5 = 105x = 10  x = (  x ) 2 = ( 5 ) 2 x = 5 x = 2 x = 25 (5) + 5 = 105(2) = 10  25 = 5 10 = = 10 5 = 5.

GET READY-MATH UNIT WIKI. Wiki SOLVING EXPONENTIAL AND LOGARITHMIC EQUATIONS.

EXAMPLE 1 Solve a system graphically Graph the linear system and estimate the solution. Then check the solution algebraically. 4x + y = 8 2x – 3y = 18.

EXAMPLE 1 Solve an equation with two real solutions Solve x 2 + 3x = 2. x 2 + 3x = 2 Write original equation. x 2 + 3x – 2 = 0 Write in standard form.

Solving Exponential and Logarithmic Equations Section 3.4.

Example 1 Solve Using Equal Powers Property Solve the equation. a. 4 9x = – 4 x x23x = b. Write original equation. SOLUTION a. 4 9x 5 42.

8.5 – Exponential and Logarithmic Equations

Ch. 8.5 Exponential and Logarithmic Equations

1. Add: 5 x2 – 1 + 2x x2 + 5x – 6 ANSWERS 2x2 +7x + 30

4.6 Type 2 Exponential Equations

EXAMPLE 2 Rationalize denominators of fractions Simplify

8.5 – Exponential and Logarithmic Equations

( ) EXAMPLE 3 Standardized Test Practice SOLUTION 5 x = – 9 – 9

Solve an equation by multiplying by a reciprocal

Solve a quadratic equation

8.6 Solving Exponential & Logarithmic Equations

Solve an equation with two real solutions

A quadratic equation is written in the Standard Form,

Logarithmic and exponential equations

Logarithmic and Exponential Equations

Solving a Radical Equation

Chapter 5: Exponential and Logarithmic Functions

Solving Logarithmic Equations

Using Properties of Logarithms

Logarithmic and exponential equations

3(9z + 4) > 35z – 4 Original problem. Solve each inequality. Then graph the solution set on the number line. 3(9z + 4) > 35z – 4 Original problem.

Definition of logarithm

Exponential Equations

Exponential Equations

Equations Involving Absolute Value

Presentation transcript:

More Exponential and Logarithmic Equations We’re right in with more practice problems in Sec. 3.5b

Solve Multiply both sides of the equation by

Solve Let Quadratic Formula!!!

Solve Because is always positive, we reject the possibility that has the negative value Can we verify this answer graphically???

Solve When solving logarithmic equations, you may introduce extraneous solutions, or even lose some valid solutions! Method 1 – Use the one-to-one property of logarithms.

Solve When solving logarithmic equations, you may introduce extraneous solutions, or even lose some valid solutions! Method 2 – Change the equation to exponential form.

Solve When solving logarithmic equations, you may introduce extraneous solutions, or even lose some valid solutions! Method 3 – Use the power rule of logarithms. An incorrect solution!!! Check the graph???

Solve x = 1/2 or 2 Extraneous!!! SupportGraphically!!!

Guided Practice Solve the given equation.

Guided Practice Solve the given equation. Multiply both sides by :

Guided Practice Solve the given equation.

Guided Practice Solve the given equation.

Guided Practice Solve the given equation. Use the quad. form.!!!

Guided Practice Solve the given equation. In the original equation, x must be positive, so the only actual solution: