daily warm-up quiz 1.expand: ln x -5 y 2 2x 2. condense: ½ ln4 + 2 (ln6-ln2) 3. use properties of...
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![Page 1: Daily Warm-UP Quiz 1.Expand: ln x -5 y 2 2x 2. Condense: ½ ln4 + 2 (ln6-ln2) 3. Use properties of logs to solve for x: a. log 81 = x log3 b. log x 8/64](https://reader030.vdocuments.mx/reader030/viewer/2022032605/56649e7c5503460f94b7de97/html5/thumbnails/1.jpg)
Daily Warm-UP Quiz
1. Expand: ln x -5 y2
2x
2. Condense: ½ ln4 + 2 (ln6-ln2)
3. Use properties of logs to solve for x: a. log 81 = x log3 b. logx 8/64 = -3Answers: 1.) 2 lny – ln2 – 6 lnx 2.) ln 18 3a.) x = 4; 3b.) x = 2
![Page 2: Daily Warm-UP Quiz 1.Expand: ln x -5 y 2 2x 2. Condense: ½ ln4 + 2 (ln6-ln2) 3. Use properties of logs to solve for x: a. log 81 = x log3 b. log x 8/64](https://reader030.vdocuments.mx/reader030/viewer/2022032605/56649e7c5503460f94b7de97/html5/thumbnails/2.jpg)
Solving Exponential and Logarithmic
EquationsPart I: During this lesson, you will solve exponential equations.
![Page 3: Daily Warm-UP Quiz 1.Expand: ln x -5 y 2 2x 2. Condense: ½ ln4 + 2 (ln6-ln2) 3. Use properties of logs to solve for x: a. log 81 = x log3 b. log x 8/64](https://reader030.vdocuments.mx/reader030/viewer/2022032605/56649e7c5503460f94b7de97/html5/thumbnails/3.jpg)
Inverse Properties of Exponents and Logarithms
Let a be a positive real number; a ≠ 1.
Base a1. loga ax = ___
2. alogax = x
Base eln ex = ___e lnx = x
xx xx
![Page 4: Daily Warm-UP Quiz 1.Expand: ln x -5 y 2 2x 2. Condense: ½ ln4 + 2 (ln6-ln2) 3. Use properties of logs to solve for x: a. log 81 = x log3 b. log x 8/64](https://reader030.vdocuments.mx/reader030/viewer/2022032605/56649e7c5503460f94b7de97/html5/thumbnails/4.jpg)
Example 1: Solving an Exponential Equation
Solve ex = 72.
![Page 5: Daily Warm-UP Quiz 1.Expand: ln x -5 y 2 2x 2. Condense: ½ ln4 + 2 (ln6-ln2) 3. Use properties of logs to solve for x: a. log 81 = x log3 b. log x 8/64](https://reader030.vdocuments.mx/reader030/viewer/2022032605/56649e7c5503460f94b7de97/html5/thumbnails/5.jpg)
Example 2: Solving an Exponential Equation
Solve 10x + 5 = 60.
![Page 6: Daily Warm-UP Quiz 1.Expand: ln x -5 y 2 2x 2. Condense: ½ ln4 + 2 (ln6-ln2) 3. Use properties of logs to solve for x: a. log 81 = x log3 b. log x 8/64](https://reader030.vdocuments.mx/reader030/viewer/2022032605/56649e7c5503460f94b7de97/html5/thumbnails/6.jpg)
Example 3: Solving an Exponential Equation
Solve 4e 2x = 5
![Page 7: Daily Warm-UP Quiz 1.Expand: ln x -5 y 2 2x 2. Condense: ½ ln4 + 2 (ln6-ln2) 3. Use properties of logs to solve for x: a. log 81 = x log3 b. log x 8/64](https://reader030.vdocuments.mx/reader030/viewer/2022032605/56649e7c5503460f94b7de97/html5/thumbnails/7.jpg)
Final Check for Understanding
1. Explain how to solve 2x = 10 by taking the log of both sides of the equation.
Homework Assignment:
![Page 8: Daily Warm-UP Quiz 1.Expand: ln x -5 y 2 2x 2. Condense: ½ ln4 + 2 (ln6-ln2) 3. Use properties of logs to solve for x: a. log 81 = x log3 b. log x 8/64](https://reader030.vdocuments.mx/reader030/viewer/2022032605/56649e7c5503460f94b7de97/html5/thumbnails/8.jpg)
Daily Warm-UP Quiz
1. What are two ways to determine if an equation is an exponential equation?
2. Describe the step-by-step procedure for solving an exponential equation.
3. Use Properties of Logs Properties of Logs to solve for x:
logx 27/64= 3
4. Expand the expression: (2x/x2)3
![Page 9: Daily Warm-UP Quiz 1.Expand: ln x -5 y 2 2x 2. Condense: ½ ln4 + 2 (ln6-ln2) 3. Use properties of logs to solve for x: a. log 81 = x log3 b. log x 8/64](https://reader030.vdocuments.mx/reader030/viewer/2022032605/56649e7c5503460f94b7de97/html5/thumbnails/9.jpg)
Solving Exponential and Logarithmic
EquationsPart II: During this lesson, you will solve logarithmic
equations.
![Page 10: Daily Warm-UP Quiz 1.Expand: ln x -5 y 2 2x 2. Condense: ½ ln4 + 2 (ln6-ln2) 3. Use properties of logs to solve for x: a. log 81 = x log3 b. log x 8/64](https://reader030.vdocuments.mx/reader030/viewer/2022032605/56649e7c5503460f94b7de97/html5/thumbnails/10.jpg)
Before we start recall Inverse Properties of Exponents and Logarithms:
![Page 11: Daily Warm-UP Quiz 1.Expand: ln x -5 y 2 2x 2. Condense: ½ ln4 + 2 (ln6-ln2) 3. Use properties of logs to solve for x: a. log 81 = x log3 b. log x 8/64](https://reader030.vdocuments.mx/reader030/viewer/2022032605/56649e7c5503460f94b7de97/html5/thumbnails/11.jpg)
Solving Logarithmic Equations
NOTE: To solve a logarithmic equation such as
ln x = 3, we write the equation in exponential form as follows:
e ln x = e3
x = e3
This procedure is called exponentiating both sides of the equation.
![Page 12: Daily Warm-UP Quiz 1.Expand: ln x -5 y 2 2x 2. Condense: ½ ln4 + 2 (ln6-ln2) 3. Use properties of logs to solve for x: a. log 81 = x log3 b. log x 8/64](https://reader030.vdocuments.mx/reader030/viewer/2022032605/56649e7c5503460f94b7de97/html5/thumbnails/12.jpg)
Example 4: Solving a Logarithmic Equation
Solve 5 + 2 ln x = 4.
![Page 13: Daily Warm-UP Quiz 1.Expand: ln x -5 y 2 2x 2. Condense: ½ ln4 + 2 (ln6-ln2) 3. Use properties of logs to solve for x: a. log 81 = x log3 b. log x 8/64](https://reader030.vdocuments.mx/reader030/viewer/2022032605/56649e7c5503460f94b7de97/html5/thumbnails/13.jpg)
Example 5: Solving a Logarithmic Equation
Solve 2 log 10 3x = 4.
![Page 14: Daily Warm-UP Quiz 1.Expand: ln x -5 y 2 2x 2. Condense: ½ ln4 + 2 (ln6-ln2) 3. Use properties of logs to solve for x: a. log 81 = x log3 b. log x 8/64](https://reader030.vdocuments.mx/reader030/viewer/2022032605/56649e7c5503460f94b7de97/html5/thumbnails/14.jpg)
Example 6: Doubling Time
You have deposited $500 in an account that pays 6.75% interest, compounded continuously. How long will it take for your money to double?A = ____; P = ____; r = ____ t = ___
A = Pert
![Page 15: Daily Warm-UP Quiz 1.Expand: ln x -5 y 2 2x 2. Condense: ½ ln4 + 2 (ln6-ln2) 3. Use properties of logs to solve for x: a. log 81 = x log3 b. log x 8/64](https://reader030.vdocuments.mx/reader030/viewer/2022032605/56649e7c5503460f94b7de97/html5/thumbnails/15.jpg)
Final Check for Understanding
Explain how to solve log 10 x = 2.4 by exponentiating both sides of the equation.
Homework Assignment: