1. Welcome to class Your warm up is on the back table.
Please get started.
We’ll go over it in a minute.

2. Solving Exponential Equations

3. Definition An exponential equation is an equation in which
a variable appears
in the exponent.
Examples of exponential equations
2x = 4
22x = 16
2x + 1 = 256

4. Types of exponential equations
There are many different kinds of exponential equations.
Today, we’ll focus on exponential equations that have a single term on both sides.
These equations can be classified into two different types:
Type #1) When the bases are of both terms are the same
Type #2) When the bases are of the terms are different

5. Type #1) When the bases of both terms are the same, solve by equating exponents
Bases are the same
Equate the exponents
Solve
Check
Sweet

6. 53 – 2x = 5-x 3 – 2x = -x 3 = x 53 – 2(3) = 5-3 53 – 6= 5-3 5-3 = 5-3
Let me show you again
53 – 2x = 5-x
Bases are the same
3 – 2x = -x
Equate the exponents
3 = x
Solve
53 – 2(3) = 5-3
53 – 6= 5-3
5-3 = 5-3
Nice
Check

7. Whiteboards Your turn Bases are the same Check Solve
Equate the exponents
Check
Solve
Whiteboards

8. McAnelly’s Incredibly Awesome Timer1 2 3 1 5 4 2 7 6 8 9 1 5 6 4 3 5 2 9 4 5 3 2 1 6 7 2 3 1 8 7 4 1 9 1 8 7 8 6 2 3 8 9 7 6 4 5 4 5 3 4 2 9 3 5 1 2 6 9 8 7
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9. McAnelly’s Incredibly Awesome Timer1 3 1 5 4 2 7 6 8 9 1 5 6 4 3 5 2 9 4 5 3 2 1 6 7 2 3 1 8 7 4 1 9 1 8 7 8 6 2 3 8 9 7 6 4 5 4 5 3 4 2 9 3 5 1 2 6 9 8 7
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11. Your turn X = -2 X = 6 X = -8 Bases are the same Check Solve
Equate the exponents
Check
Solve
X = -2
X = 6
X = -8

12. Rewrite so that bases are the same
Type #2) When the bases are different , rewrite the expressions to have the same base
Rewrite so that bases are the same
2(3x) = 3(x + 1)
Equate the exponents
6x = 3x + 3
Solve
Beautiful
Check

13. Rewrite so that bases are the same
Let me show you again
43 =2x
Rewrite so that bases are the same
22(3) = 2x
Equate the exponents
2(3) = x
6 = x
Solve
43 = 26
22(3)= 26
26 = 26
Easy
Check

14. Rewrite so that bases are the same
Let’s kick it up a notch
32-r = 1
Rewrite so that bases are the same
32-r = 30
Equate the exponents
2-r = 0
r = 2
Solve
32-2 = 1
30 = 1
1 = 1
Woot
Check

15. REWRITE so bases are the same
Your turn
REWRITE so bases are the same
Grab a calculator
Equate the exponents
Solve
Check
4 𝑥 −2 = 8 𝑥 −5
16 2𝑥 −1 = 64 3𝑥+8
25 2𝑥 = 125 𝑥+10
X = 11 3
X = -6
X = 30

16. Rewrite so that bases are the same
One for the money
Solve this on your board.
Turn it over when you are done.
I will walk around and check.
36(x+2) = 216(x-1)
Rewrite so that bases are the same
36(7+2) = 216(7-1)
369= 2166
Verified with calculator
62(x+2) = 63(x-1)
Equate the exponents
2(x+2) = 3(x-1)
Solve
2x+4 = 3x-3
Check
x= 7

17. Solving Exponential Equations - EASY
Your assignment
Solving Exponential Equations - EASY