Solving Exponential and Logarithmic EquationsSection 8.6

Objectives

•Solve exponential equations.•Solve logarithmic equations.•Use exponential and logarithmic functions

to model real-life situations.

Solving Exponential EquationsTime to think … Hmmm…?

•If two powers with the same base are equal … what can we conclude about their exponents?

Their exponents must be equal!

𝑏𝑥=𝑏 𝑦

Applying the Concept What must x equal in order for the left side

to equal the right side?

𝑥=4

𝑥=2

𝑥=1

𝑥=3

Applying the Concept

•Keep in mind that these two numbers are equal. If the bases are the same, then their exponents must be the same too!

22 𝑥=2𝑥+3

2 𝑥=𝑥+3𝑥=3

Different Bases• How do we address examples with different

bases?• We need to create a common base!43 𝑥=8𝑥+1 How can we transform 4

and 8 into the same base number with different

exponents?(22 )3𝑥=(23 )𝑥+1

26 𝑥=23𝑥+3

6 𝑥=3 𝑥+33 𝑥=3𝑥=1

Solving by Equating ExponentsSolve the equation.

23 𝑥=4𝑥−1 92𝑥=3𝑥−6

𝑥=−2 𝑥=−2

Solving by Equating ExponentsSolve the equation.

2𝑥=7We may not be able to create common bases and equate exponents every time.

Solving by … Taking a LogarithmSolve the equation.

2𝑥=7What will “undo,” or cancel out, an exponential function with a base of 2?

Hint:

log 22𝑥=log27

𝑥=log 27

𝑥=log 7log 2

𝑥≈2.807

Solving by Taking a LogarithmSolve the equation.

102𝑥− 3+4=21

𝑥≈2.12

Treasure Raffle Pairs PracticeSolve the equations.• Work in your pairs• Numbers will be selected randomly for students to present their answers and get a

chance to win extra credit

1) 𝑥=1

2)

3)

4)

𝑥=163≈5.33

𝑥=32=1.5

𝑥≈0.35

Homework

•pg. 505 #26-42 even

•Chapter 8 Test on Monday, April 22nd