Solving Exponential and Logarithmic Equations Section 8.6.

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Solving Exponential and Logarithmic Equations Section 8.6

Transcript of Solving Exponential and Logarithmic Equations Section 8.6.

Page 1: Solving Exponential and Logarithmic Equations Section 8.6.

Solving Exponential and Logarithmic EquationsSection 8.6

Page 2: Solving Exponential and Logarithmic Equations Section 8.6.

Objectives

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

to model real-life situations.

Page 3: Solving Exponential and Logarithmic Equations Section 8.6.

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

Page 4: Solving Exponential and Logarithmic Equations Section 8.6.

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

Page 5: Solving Exponential and Logarithmic Equations Section 8.6.

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

Page 6: Solving Exponential and Logarithmic Equations Section 8.6.

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

Page 7: Solving Exponential and Logarithmic Equations Section 8.6.

Solving by Equating ExponentsSolve the equation.

23 𝑥=4𝑥−1 92𝑥=3𝑥−6

𝑥=−2 𝑥=−2

Page 8: Solving Exponential and Logarithmic Equations Section 8.6.

Solving by Equating ExponentsSolve the equation.

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

Page 9: Solving Exponential and Logarithmic Equations Section 8.6.

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

Page 10: Solving Exponential and Logarithmic Equations Section 8.6.

Solving by Taking a LogarithmSolve the equation.

102𝑥− 3+4=21

𝑥≈2.12

Page 11: Solving Exponential and Logarithmic Equations Section 8.6.

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

Page 12: Solving Exponential and Logarithmic Equations Section 8.6.

Homework

•pg. 505 #26-42 even

•Chapter 8 Test on Monday, April 22nd