WarmUp

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Warm-Up
6.5 Applications of Common Logarithms

• Solve each equation for x. Round your answers to
  the nearest hundredth.
• 10x 32
• 10x 1.76
• Find the value of x in each equation below.
• -3 log10x
• 2 logx49

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Objectives
6.5 Applications of Common Logarithms

• Define and use the common logarithmic function to
  solve exponential and logarithmic equations.
• Evaluate logarithmic expressions by using the
  change-of-base formula.

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Example 1
6.5 Applications of Common Logarithms

• Solve 3x 19 for x. Round your answer to the
  nearest hundredth.

3x 19
log 3x log 19
x log 3 log 19
? 2.68
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Example 2
6.5 Applications of Common Logarithms

• Solve 32x1 212 for x. Round your answer to
  the nearest hundredth.

32x1 212
log 32x1 log 212
(2x 1) log 3 log 212
? 4.88
x ? 1.94
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Practice
6.5 Applications of Common Logarithms

• Solve 8x 792 for x. Round your answer to the
  nearest hundredth.

8x 792
log 8x log 792
x log 8 log 792
? 3.21
x ? 3.21
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Activity
6.5 Applications of Common Logarithms

• Write 3x 81 as a logarithmic expression for x
  in base 3.

log3 81 x
Write 3x 81 as a logarithmic expression for x
in base 10.
log 3x log 81
x log 3 log 81
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Activity
6.5 Applications of Common Logarithms

• Set your expressions for x from Steps 1 and 2
  equal to each other.

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Example 3
6.5 Applications of Common Logarithms

• Evaluate log7 3. Round your answer to the
  nearest hundredth.

? 0.56
log7 3
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Example 4
6.5 Applications of Common Logarithms

• Evaluate log2 12. Round your answer to the
  nearest hundredth.

? 3.58
log2 12
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Homework
6.5 Applications of Common Logarithms

• p.389-390 11,12,17,20,22,23,29,32,33,39,41