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

Solving Exponential Equations

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

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 Bases are the same Equate the exponents Solve Check Sweet

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

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

McAnelly’s Incredibly Awesome Timer 1 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 Hours Minutes Seconds

McAnelly’s Incredibly Awesome Timer 1 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 Hours Minutes Seconds

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

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

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

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

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

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

Solving Exponential Equations - EASY Your assignment Solving Exponential Equations - EASY