Chapter 10: Q48. (page 528)

Solve the inequality $2^{2 n} \leq \frac{1}{16}$ . Check your solution.

Short Answer

Expert verified

The solution for the inequality is $n \leq - 2$ .

Step by step solution

Step 1. Write down the given inequality.

The given inequality is $2^{2 n} \leq \frac{1}{16}$ .

Step 2. Simplify the inequality.

The given inequality $2^{2 n} \leq \frac{1}{16}$ is solved as:

$\begin{array}{l} 2^{2 n} \leq \frac{1}{16} .... (Given) \\ 2^{2 n} \leq 16^{- 1} \\ 2^{2 n} \leq {(2^{4})}^{- 1} \\ 2^{2 n} \leq 2^{- 4} \\ 2 n \leq - 4 \\ n \leq - 2 \end{array}$

Step 3. Verify the result for obtained value.

Plugging $n = - 2$ in given inequality and verify the result.

$\begin{array}{l} 2^{2 n} \leq \frac{1}{16} .... (Given) \\ 2^{2 (- 2)} \leq \frac{1}{16} \\ 2^{- 4} \leq \frac{1}{16} \\ \frac{1}{2^{4}} \leq \frac{1}{16} \\ \frac{1}{16} \leq \frac{1}{16} .... (True) \end{array}$

Hence the solution is verified for $n \leq - 2$ .

Step 4. Conclusion.

The solution for the given inequality is $n \leq - 2$ .

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Solve the inequality $2^{2 n} \leq \frac{1}{16}$ . Check your solution.

Short Answer

Step by step solution

Step 1. Write down the given inequality.

Step 2. Simplify the inequality.

Step 3. Verify the result for obtained value.

Step 4. Conclusion.

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Solve the inequality 22n≤116. Check your solution.

Short Answer

Step by step solution

Step 1. Write down the given inequality.

Step 2. Simplify the inequality.

Step 3. Verify the result for obtained value.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

Solve the inequality $2^{2 n} \leq \frac{1}{16}$ . Check your solution.