Solve Exponential and Logarithmic Inequalities - PowerPoint PPT Presentation

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Solve Exponential and Logarithmic Inequalities

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Solve Exponential and Logarithmic Inequalities Vocabulary An exponential inequality in one variable is an inequality that can be written in the form abx + k – PowerPoint PPT presentation

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Title: Solve Exponential and Logarithmic Inequalities


1
Solve Exponential and Logarithmic Inequalities
2
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.

3
Solving Exponential and Logarithmic Inequalities
  • You can use the same methods used to solve
    polynomial inequalities in Lesson 2.4!

4
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)

5
You Try
  • Solve the exponential inequality
  • 32x 1 lt 4
  • 73x 4 lt 18

6
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?
7
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)

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

9
Homework
  • P. 167 1-18
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