Solve Exponential and Logarithmic Inequalities

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Solve Exponential and Logarithmic Inequalities
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Vocabulary

• An exponential inequality in one variable is an
  inequality that can be written in the form abx
  k lt 0, abx k lt 0, abx k gt 0, or abx k gt 0,
  where a 0, b gt 0, and b 1.
• A logarithmic inequality in one variable is an
  inequality that can be written in the form logbx
  k lt 0, logbx k lt 0,
  logbx k gt 0, or logbx k gt 0, where b
  gt 0, and b 1.

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Solving Exponential and Logarithmic Inequalities

• You can use the same methods used to solve
  polynomial inequalities in Lesson 2.4!

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Example 1

• Solve 4x 1 gt 32
• Step 1 Write the equation that corresponds to
  inequality.
• Step 2 Solve for x.
• Step 3 plot the x-value on a number line and
  test intervals
• 1.5, 8)

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You Try

• Solve the exponential inequality
• 32x 1 lt 4
• 73x 4 lt 18

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Example 2

• Solve the logarithmic inequality
• log5x lt 2
• Step 1 Write the corresponding equation
• Step 2 solve for x.
• Step 3 plot the x-value on a number line and
  test intervals
• (0, 25)

WATCH OUT! How many x-values should you plot on
the number line?
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Example 2 Contd

• Solve the logarithmic inequality
• log4x 8 gt 11
• Step 1 Write the corresponding equation
• Step 2 solve for x.
• Step 3 plot the x-value on a number line and
  test intervals
• 64, 8)

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You Try

• Solve the logarithmic inequalities
• log62x 7 lt 10
• log9(x 8) gt 3/2

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Homework

• P. 167 1-18