1. 8.5 – Exponential and Logarithmic Equations

2. CHANGE OF BASE FORMULA
where M, b, and c are positive numbers and b, c do not equal one.
Ex: Rewrite log515 using the change of base formula

3. Steps for solving exponential equations
Take a common logarithm of each side
Use the power property of logarithms
Solve for x by dividing
Use a calculator to find the approximate value

4. Solving Exponential Equations
Solve Round to the nearest ten-thousandth.
1. Take the log of both sides
2. Use the power property
3. Solve for x.
X=1.2619
4. Use a calculator.
Check your answer – =4

5. Another Example Solve . Round to the nearest ten-thousandth.
1. Take the log of both sides
2. Use the power property
3. Solve for x.
X= – 4 =
4. Use a calculator.
Check your answer – =101

6. Let’s try some

7. Let’s try some

8. Let’s try some

9. Let’s try some

10. CHANGE OF BASE – HOW IT WORKS
Use the change of base formula to evaluate Then convert it to a logarithm of base 2.
1. Rewrite using the change of base formula
2. Use a calculator
3. Write an equation to convert to base 2

11. CHANGE OF BASE – HOW IT WORKS
4. Substitute log315=2.4650
5. Rewrite using the change of base formula
6. Multiply both sides of the equation by log2
7. Use a calculator; simplify.
8. Write in exponential form.
X=5.5208
9. Use a calculator.
Log315 is approximately equal to or log

12. Let’s try one
Use the change of base formula to evaluate Then convert it to a logarithm of base 8.
1. Rewrite using the change of base formula
2. Use a calculator
3. Write an equation to convert to base 2

13. 4. Substitute log5400=3.727
5. Rewrite using the change of base formula
6. Multiply both sides of the equation by log8
7. Use a calculator; simplify.
8. Write in exponential form.
X=2301
9. Use a calculator.
Log5400 is approximately equal to or log82301

14. SOLVING SIMPLE LOG EQUATIONS
1. Use the product property
2. Write in exponential form.
3. Simplify
4. Solve for x.

15. Let’s try some

16. Let’s try some

17. Let’s try some

18. Let’s try some

19. Solving exponential equations with a graphing calculator
Type two equations into y=
2. Graph. Suggest Zoom fit (0)
especially for large values
3. Use the calc function to find the intersection of the two graphs.
Solution: