1. Solving Exponential Equations

2. Real World Use of
Exponential Functions
•
•
•
•
•
Population Growth
Money (Compound Interest)
Depreciation (Cars)
Half-Life (Radioactive Material)
Bacteria Growth

3. Exponential Equations
• One way to solve exponential
equations is to use the property that if
2 powers w/ the same base are equal,
then their exponents are equal.
• For b>0 & b≠1 if
x
b
=
y,
b
then x=y

4. Solve by equating
exponents
3x 3
9
2
2
3x 3 9
x
4
Since they have the same
bases we can set their
exponents equal to each
other and solve for x.
34 3
Check → 2
29
29
9
2

5. Your turn

6. Solve by equating exponents
3x
4
2
8
2 3x
6x
2
x 1
3 x 1
2
3x 3
2
Distribute!
Since they do NOT
have the same
bases…we have to
rewrite so they have
common bases.
Common base = 2
6x 3x 3
31
x 1
4
81 1
Check →
64 64

7. Your turn

8. Solve by equating exponents
4
x
1
2
2 x
2
2
2x
2x
2
2
x 3
Common base = 2
1x 3
Distribute!
x 3
How can we make ½ a
base of 2?
Negative exponents!!!
x 3
1
2
1
Check →
4
4
x 1
1
2
4
4
22
4
1 3
2

9. You Try

10. Your turn!
9
x
3
x 2
Be sure to check your answer!!!
x
2

11. Your turn!
3
1 x
( )
9
x
3
Be sure to check your answer!!!
x
2

12. Your turn!
9
x 4
27
4x
Be sure to check your answer!!!
x
4
5

13. H/W
p.488 #9,10,12,14,32,33