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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
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