Exponential and Logarithmic Equations

1. Exponential and Logarithmic Equations Section 3.4

2. Objectives • Solve a logarithmic equation. • Solve an exponential equation.

3. OR Solve the equation Change to logarithmic form Take the logarithm of both sides of the equation OR

4. Solve the equation Change to logarithmic form Take the logarithm of both sides of the equation OR

5. OR OR Solve the equation Solve using factoring Change to logarithmic form Take the logarithm of both sides of the equation negative numbers are not in the domain of a logarithm negative numbers are not in the domain of a logarithm

6. OR OR Solve the equation Solve using the quadratic formula Change to logarithmic form Take the logarithm of both sides of the equation negative numbers are not in the domain of a logarithm negative numbers are not in the domain of a logarithm

7. Initial population is 2310 bacteria. The number of bacteria in a culture is modeled bywhere t is in hours. • What is the initial number of bacteria? • What is the relative growth rate of the bacterium population The relative growth rate is .54 or 54%.

8. The population in three hours will be 11673 bacteria. Note: 11672 bacteria would also be accepted. The number of bacteria in a culture is modeled bywhere t is in hours. • How many bacteria will there be in three hours?

9. It will take 2.713589 hours for there to be 10000 bacteria. The number of bacteria in a culture is modeled bywhere t is in hours. • How many hours will it take for there to be 10000 bacteria?

10. Solve the equation Change to exponential form Exponentiate both sides of the equation OR

11. Solve the equation Change to exponential form Exponentiate both sides of the equation OR

12. Continued Solve the equation Check possible solutions in original equation arguments are both positive negative numbers are not in the domain of a logarithm only solution is

13. Solve the equation Factoring Change to exponential form Exponentiate both sides of the equation OR Check answers in original equation Both answers are good.

14. Solve the equation Quadratic Formula Change to exponential form Exponentiate both sides of the equation OR

15. Continued Solve the equation Quadratic Formula Check answers in original equation Both answers are good.

16. Solve the equation 0 is not in the domain of a logarithm only solutions are

17. Solve the equation Change to logarithmic form We will assume that the left side is the exponential function change of base

18. Solve the equation Change to logarithmic form We will assume that the right side is the exponential function change of base

19. Solve the equation Take the logarithm of both sides of the equation

20. Solve the equation Change to logarithmic form Take the logarithm of both sides of the equation OR change of base

21. Solve the equation Move all logarithms to one side and combine using the Laws of Logarithms

22. Solve the equation Move all logarithms to one side and combine using the Laws of Logarithms - Continued Change to logarithmic form Take the logarithm of both sides of the equation OR

23. Solve the equation Move all logarithms to one side and combine using the Laws of Logarithms - Continued Check answers in original equation 0 is not in the domain of a logarithm only valid answer is x = 32

24. Solve the equation Combine logarithms to have a single logarithm on each side Exponentiate both sides of the equation

25. Solve the equation Combine logarithms to have a single logarithm on each side – Continued Check answers in original equation 0 is not in the domain of a logarithm only valid answer is x = 32