Transcript Algebra Animated for Teachers!

Solving Exponential Equations
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
Solve by equating
exponents
3 x3
2
2
9
3x  3  9
x4
Since they have the same
bases we can set their
exponents equal to each
other and solve for x.
3 4  3
2
9
Check → 2
2 2
9
9
Your turn
• 22𝑥 = 2𝑥 −2
• 56𝑥 −4 = 54𝑥+8
• 72𝑥 −1 = 73𝑥+7
Solve by equating exponents
4 8
3x
2 3 x 
2
x1
3 x1
2
2 2
6x
3 x 3
6 x  3x  3
x 1
Distribute!
Since they do NOT
have the same
bases…we have to
rewrite so they have
common bases.
Common base = 2
31
11
4

8
Check →
64  64
Your turn
• 4𝑥 −2 = 8𝑥 −5
• 162𝑥 −1 = 643𝑥+8
• 252𝑥 = 125𝑥+10
Solve by equating exponents
1
4  
2
x 3
x
2
2 x 
2
2 2
2x
1 x3
Common base = 2
Distribute!
 x 3
Negative exponents!!!
2x  x  3
1 3
1
4  
2
1
Check →
x 1
How can we make ½ a
base of 2?
1
4 
2
4  22
44
2
You Try
• 2
𝑥−6
• 4
3𝑥
−𝑥
•3
=
=
=
1 4
( )
8
1 15
( )
16
1 2𝑥+5
( )
27
Your turn!
9 3
x
x 2
Be sure to check your answer!!!
x2
Your turn!
1 x3
3 ( )
9
x
Be sure to check your answer!!!
x2
Your turn!
9
x4
 27
4x
Be sure to check your answer!!!
4
x
5
Practice/H.W.
Solving Exponential Equations
WS