1. Exponential & Logarithmic Functions
CHAPTER 4
Exponential & Logarithmic Functions

2. Before we can talk about logs we need to do some review…
LAWS OF EXPONENTS

3. Law #1
xmxn = xm+n
Example: x2x3
x2x3 = x(2+3) = x5

4. Law #2
xm/xn = xm-n
Example: x4/x2
x4/x2 = x(4-2) = x2

5. Law #3
(xm)n = xmn
Example: (x3)4
(x3)4 = x(3x4) = x12

6. Law #4
(xy)n = xnyn
Example: (xy)3
(xy)3 = x3y3

7. Law #5
xm/n = xn/yn
Example: (x/y)3
(xy)3 = x3/y3

8. Law #6
Example:

9. Law #7
x-m = 1/xm
Example: x-3
x-3 = 1/x3

10. Solving Exponential Equation
An exponential equation is one in which a variable occurs in the exponent.

11. Solving Exponential Equation
An equation in which each side can be expressed in terms of the same base can be solved using the property:
bx = by
Then x=y (and solve…)

12. Example 1
5x = 53
So… x=3

13. Example 2
101-x = 104
So… 1-x=4
1-4 = x
-3 = x

14. Example 3
2x = 32
2x = 25
x = 5
Express as a base 2!

15. Example 4 32x-1 = 27 32x-1 = 33 2x-1 = 3 2x = 4 x = 2
Express as a base 3

16. Example 5 (3x)2x+2 = 81 (3)2x2+2x = 34 2x2 + 2x = 4 2x2 + 2x – 4 = 0

17. Example 6 4x+1 = 1/64 *note 64=43 So 1/64 = 4-3 4x+1 = 4-3 x + 1 = -3

18. WORKSHEET side 1 (solve for x…)
HOMEWORK
WORKSHEET side 1 (solve for x…)
KEEP THIS SHEET!