2. Chapter 5 Lesson 3 Exponential and Logarithmic Equations

3. Solving Exponential Equations Using Logarithmic Forms  To solve an exponential equation using logarithmic form: 1. Rewrite the equation with the term containing the exponent by itself on one side 2. Divide both sides by the coefficient of the term containing the exponent 3. Change the new equation to logarithmic form 4. Solve for the variable

4. Solving a Base 10 Exponential Equation

5. Doubling Time

6. Carbon-14 Dating

7. Change of Base  Most calculators and other graphing utilities can be used to evaluate logarithms and graph logarithmic functions if the base is 10 or e.  Graphing logarithmic functions with other bases usually requires converting to exponential form to determine outputs and then graphing the functions by plotting points by hand.  However, we can use a special formula called the change of base formula to rewrite logarithms so that the base is 10 or e.

8. Change of Base Formula

10. Applying the Change of Base Formula

11. Investment

12. Solving Exponential Equations Using Logarithmic Properties  To solve an exponential equation using logarithmic properties: 1. Rewrite the equation with a base raised to a power on one side 2. Take the logarithm, base e or 10, of both sides of the equation 3. Use a logarithmic property to remove the variable from the exponent 4. Solve for the variable

13. Solution of Exponential Equations

14. Solution of Logarithmic Equations

15. Solving a Logarithmic Equation 1. Solve 6 + 3 ln x = 12 by writing the equation in exponential form. 2. Solve the equation graphically

16. Solving a Logarithmic Equation  Solve ln x + 3 = ln (x + 4) by converting the equation to exponential form and then using algebraic methods.

17. Global Warming

18. Sales Decay

19. Cost-Benefit

20. Homework  Pages 358-360  1-29 odd,31-33,43,47,51,53-55,63