1. 2. Condense: ½ ln4 + 2 (ln6-ln2)
Daily Warm-UP Quiz
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 = -3
Answers: 1.) 2 lny – ln2 – 6 lnx
2.) ln 18
3a.) x = 4; 3b.) x = 2

2. Solving Exponential and Logarithmic Equations
Part I: During this lesson, you will solve exponential equations.

3. Inverse Properties of Exponents and Logarithms
Let a be a positive real number; a ≠ 1.
Base a
1. loga ax = ___
2. alogax = x
Base e
ln ex = ___
e lnx = x x x

4. Example 1: Solving an Exponential Equation
Solve ex = 72.

5. Example 2: Solving an Exponential Equation
Solve 10x + 5 = 60.

6. Example 3: Solving an Exponential Equation
Solve 4e 2x = 5

7. Final Check for Understanding
1. Explain how to solve 2x = 10 by taking the log of both sides of the equation.
Homework Assignment:

8. Daily Warm-UP Quiz
What are two ways to determine if an equation is an exponential equation?
Describe the step-by-step procedure for solving an exponential equation.
Use Properties of Logs to solve for x:
logx 27/64= 3
4. Expand the expression: (2x/x2)3

9. Solving Exponential and Logarithmic Equations
Part II: During this lesson, you will solve logarithmic equations.

10. Before we start recall Inverse Properties of Exponents and Logarithms:

11. 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.

12. Example 4: Solving a Logarithmic Equation
Solve ln x = 4.

13. Example 5: Solving a Logarithmic Equation
Solve 2 log 10 3x = 4.

14. 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

15. Final Check for Understanding
Explain how to solve log 10 x = 2.4 by exponentiating both sides of the equation.
Homework Assignment: