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♥ 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