7.5 E XPONENTIAL AND L OGARITHMIC E QUATIONS AND I NEQUALITIES Solve exponential and logarithmic equations and equalities. Solve problems involving exponential.

Slides:

Advertisements

Similar presentations

Objectives Solve exponential and logarithmic equations and equalities.

Advertisements

Logarithmic Equations Unknown Exponents Unknown Number Solving Logarithmic Equations Natural Logarithms.

MAT 150 – Class #19. Objectives  Solve an exponential equation by writing it in logarithmic form  Convert logarithms using the change of base formula.

7.5 E XPONENTIAL AND L OGARITHMIC E QUATIONS. E XPONENTIAL E QUATIONS An exponential equation is an equation containing one or more expressions that have.

Questions over 4.6 HW???. 4.7 (Green) Solve Exponential and Logarithmic Equations No School: Monday Logarithms Test: 1/21/10 (Thursday)

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

Objectives Solve exponential and logarithmic equations and equalities.

Logarithmic and Exponential Equations

Section 4.5 Exp. & Log Equations

LOGS EQUAL THE The inverse of an exponential function is a logarithmic function. Logarithmic Function x = log a y read: “x equals log base a of y”

Recall: These are equations of the form y=ab x-h +k, ones where the ‘x’ is in the exponent Recall: These are equations of the form y=ab x-h +k, ones where.

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.

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

8.6 Solving Exponential and Logarithmic Equations Goal: Solve exponential and logarithmic equations. Correct WS 8.5A.

Warm up. 3.4 Solving Exponential & Logarithmic Equations Standards 13, 14.

Academy Algebra II/Trig 6.6: Solve Exponential and Logarithmic Equations Unit 8 Test ( ): Friday 3/22.

Solving Exponential and Logarithmic Equations Section 8.6.

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

1. Expand the following: 2. Condense the following: Warm-upWarm-up.

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

6.4 – Solving Logarithmic Equations and Inequalities Objective: TSW solve logarithmic equations and inequalities.

8.3-4 – Logarithmic Functions. Logarithm Functions.

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.

Solving Exponential Equations. We can solve exponential equations using logarithms. By converting to a logarithm, we can move the variable from the exponent.

For b > 0 and b ≠ 1, if b x = b y, then x = y. S OLVING E XPONENTIAL E QUATIONS If two powers with the same base are equal, then their exponents must be.

5.5Logarithms. Objectives: I will be able to…  Rewrite equations between exponential and logarithmic forms  Evaluate logarithms  Solve logarithms Vocabulary:

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

Solving Logarithmic Equations

Converting between log form and exponential form.

S OLVING E XPONENTIAL AND LOGARITHMIC E QUATIONS Unit 3C Day 5.

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

4.7 (Green) Solve Exponential and Logarithmic Equations No School: Monday Logarithms Test: 1/21/10 (Thursday)

Logarithmic Properties Exponential Function y = b x Logarithmic Function x = b y y = log b x Exponential Form Logarithmic Form.

How do we solve exponential and logarithmic equations and equalities?

Solving equations with variable on both sides Part 1.

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

LOGARITHMIC AND EXPONENTIAL EQUATIONS LOGARITHMIC AND EXPONENTIAL EQUATIONS SECTION 4.6.

S OLVING E XPONENTIAL AND LOGARITHMIC E QUATIONS Unit 3C Day 5.

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.

Ch. 8.5 Exponential and Logarithmic Equations

Solving Exponential and Logarithmic Equations

Logarithmic Functions and Their Graphs

Logarithmic Functions

Unit 8 [7-3 in text] Logarithmic Functions

Packet #15 Exponential and Logarithmic Equations

5.6 Solving Exponential and Logarithmic Equations

7.5 Exponential and Logarithmic Equations

Solving Exponential & logarithmic Equations

Exponential Functions & Introduction to Logarithmic Functions

Logarithmic and Exponential Equations

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

Inverse, Exponential and Logarithmic Functions

Logarithmic and Exponential Equations

Solving Equations with Variables on Both Sides

Solving Equations with Variables on Both Sides

bell ringer How do you “convert”?

Solving Logarithmic Equations

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.

Warm Up 1) x = 20 2) x = -8.

Definition of logarithm

Logarithmic Functions

Solve the equations. 4 2

Presentation transcript:

7.5 E XPONENTIAL AND L OGARITHMIC E QUATIONS AND I NEQUALITIES Solve exponential and logarithmic equations and equalities. Solve problems involving exponential and logarithmic equations. Objectives exponential equation logarithmic equation Vocabulary Warm Up Solve. 1. log 16 x = 2. log x = 3 3. log10,000 = x 3 2

To solve exponential equation: If the bases are the same (or can be made the same) drop the bases and solve for x. If there is only one power, switch to log equation and solve for x. If there are two powers with different bases, log both sides (base 10) and solve for x 9 8 – x = 27 x – 3 Example 1A: Solving Exponential Equations 4 x – 1 = 5 9 x = 2 2x *You can always log both sides in order to solve but might be more steps

Solve and check. 3 2 x = 27 Check It Out! Example 1a 7 –x = 21 Hint: write 27 as a power with base 3

To solve log equation, make single logs on each side of the equation and then: If the log have the same base, drop the log and solve for x. If only have one log, change to exponential equation and solve for x OR If only have one log, raise both sides to a power with the same base log 6 (x ) = 1 6 log 6 ( x ) = 6 1 Solve. Example 3: Solving Logarithmic Equations log 6 (2 x – 1) = -1 log( x + 70) = 2log ( ) x 3

Solve. Example 3B: Solving Logarithmic Equations log – log 4 (x + 1) = 1 log 5 x 4 = 8 log 12 x + log 12 ( x + 1) = 1 3 = log 8 + 3log x