The document discusses methods for solving exponential equations, emphasizing the property that if two powers with the same base are equal, their exponents must also be equal. It provides examples of solving equations by equating exponents and rewriting to find a common base when necessary. The document encourages practice with a variety of problems to solidify understanding.

1. Solving Exponential Equations

2. • 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 bx
= by
, then x=y
Exponential Equations

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

4. Your turn

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

6. Your turn

7. Solve by equating exponents
3
1
4
2
x
x

 
 
  Common base = 2
   
3
2 1
2 2
x x


2 3
2 2
x x
 

2 3
x x
 
1
x 
Check →
1 3
1
2
2
1
4
2
1
4
2
4 2
4 4


 
 
 
 
 
 


How can we make ½ a
base of 2?
Negative exponents!!!
Distribute!

8. You Try

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

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

11. Your turn!
Be sure to check your answer!!!
4 4
9 27
x x


4
5
x 

12. Practice/H.W.
Solving Exponential Equations
WS