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4.8 Solve Exponential and Logarithmic Inequalities

4.8 Solve Exponential and Logarithmic Inequalities. Inequalities Quiz: Tomorrow Inequalities Test: 3/2/10. Vocabulary.

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4.8 Solve Exponential and Logarithmic Inequalities

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  1. 4.8Solve Exponential and Logarithmic Inequalities Inequalities Quiz: Tomorrow Inequalities Test: 3/2/10

  2. Vocabulary • An exponential inequality in one variable is an inequality that can be written in the form abx + k < 0, abx + k < 0, abx + k > 0, or abx + k > 0, where a = 0, b > 0, and b = 1. • A logarithmic inequality in one variable is an inequality that can be written in the form logbx + k < 0, logbx + k < 0, logbx + k > 0, or logbx+ k > 0, where b > 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> 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, ∞)

  5. You Try: • Solve the exponential inequality • 32x – 1< 4 • 73x – 4 < 18

  6. Example 2: • Solve the logarithmic inequality • log5x < 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 Cont’d: • Solve the logarithmic inequality • log4x + 8 > 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. You Try: • Solve the logarithmic inequalities • log62x + 7 < 10 • log9(x – 8) > 3/2

  9. Homework: • P. 167 #1-18

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