1. 3.4 Exponential and Logarithmic Equations
One-to-One Properties
Inverse Property

2. One-to-One Properties
If x 6 = x y , then 6 = y
If ln a = ln b, then a = b

3. Inverse Property Given e x = 8; solve for x
Take the natural log of each side.
ln e x = ln 8
Pull the exponent in front
x ( ln e) = ln 8
(since ln e = 1)
x = ln 8

4. Solve for x 3 x = 64 take the natural log of both sides ln 3 x = ln 64
x( ln 3) = ln 64
x = ln 64 =
ln 3

5. Solve for x
e x – 8 = 70

6. Solve for x e x – 8 = 70 e x = 78 ln e x = ln 78 x = ln 78

7. Solve for a
( ¼ ) a = 64

8. Solve for K
Log 5 K = - 3

9. Solve for x
2 x – 3 = 32

10. Solve for x

11. Solve for x
e 2.724x = 29

12. Solve for a
ln a + ln ( a + 3) = 1
Will need the quadratic formula

13. Solve for x one more time
e 2x – e x – 12 = 0
factor

14. Solve for x one more time
e 2x – e x – 12 = 0
factor
(e x – 4)(e x + 3 ) = 0
So e x – 4 = 0 or e x + 3 = 0
e x = 4 e x = - 3
x = ln 4 x = ln -3

15. Homework
Page 233 – 235
# 5, 15, 25, 35,
45, 55, 65, 75,
85, 95, 105, 115,
125, 135

16. Homework
Page 233 – 235
# 10, 20, 30, 40,
50, 60, 70, 80,
90, 100, 110, 120,
130, 140