Your warm up is on the back table. Please get started. We’ll go over it in a minute.
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Transcript of Your warm up is on the back table. Please get started. We’ll go over it in a minute.
♥ Your warm up is on the back table.
♥ Please get started.
♥ We’ll go over it in a minute.
Welcome to class
4 2x + 3 = 1
Solving Exponential Equations
An exponential equation is an equation in which a variable appears in the exponent.
Definition
Examples of exponential equations2x = 4 22x = 16 2x + 1 = 256
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
Type #1) When the bases of both terms are the same,
solve by equating exponents
3 3 92 2x 3 3 9x
4x 3 4 3 9
9 9
2 2
2 2
Bases are the same
Equate the exponents
Solve
CheckSweet
Let me show you again
53 – 2x = 5-xBases are the same
Equate the exponents
Solve
Check
3 – 2x = -x
3 = x
53 – 2(3) = 5-3
53 – 6= 5-3
5-3 = 5-3
Nice
Your turnBases are the same
Equate the exponents
Solve
Check
WHITEBOARDS
09000 2 87654321510 04 98765432103 9876543210987654321021 987654321098765432100Hours Minutes Seconds
McAnelly’s Incredibly Awesome Timer
09000 1 87654321500 04 98765432103 9876543210987654321021 987654321098765432100Hours Minutes Seconds
McAnelly’s Incredibly Awesome Timer
Your turn
•
Bases are the same
Equate the exponents
Solve
Check
X = -2
X = 6
X = -8
Type #2) When the bases are different , rewrite the expressions to have the same base
3 14 8x x 3 12 32 2x x
1x
3 1 1 14 864 64
Equate the exponents
Solve
Check
Rewrite so that bases are
the same
2(3x) = 3(x + 1)6x = 3x + 3
Beautiful
Let me show you again
43 =2x 22(3) = 2x
2(3) = x
43 = 26
22(3)= 26
26 = 26
Equate the exponents
Solve
Check
Rewrite so that bases are
the same
6 = x
Easy
Let’s kick it up a notch
32-r = 1 32-r = 30
2-r = 0
32-2 = 130 = 11 = 1
Equate the exponents
Solve
Check
Rewrite so that bases are
the same
r = 2
Woot
Your turn REWRITE so bases are the same
Equate the exponents SolveCheck
X = 11
X = -6
X = 30
3
Grab a calculator
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)
62(x+2) = 63(x-1)
2(x+2) = 3(x-1)
2x+4 = 3x-3 x= 7
Equate the exponents
Solve
Check
Rewrite so that bases
are the same36(7+2) = 216(7-1)
369= 2166 Verified with calculator
Your assignment
Solving Exponential Equations - EASY