### Solving Exponential Equations **Problem Statement:** Solve the following exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. \[9^{x - 6} = 81\] **Question 1: What is the exact answer?** Select the correct choice below and, if necessary, fill in the answer box to complete your choice. - **O A. The solution set is \( \{ \_\_\_\_\_\} \).** (Simplify your answer. Type an exact answer) - **O B. There is no solution.** **Question 2: What is the answer rounded to three decimal places?** Select the correct choice below and, if necessary, fill in the answer box to complete your choice. - **O A. The solution set is \( \{ \_\_\_\_\_\} \).** (Simplify your answer. Type an integer or decimal rounded to three decimal places as needed.) - **O B. There is no solution.** *Click to select and enter your answer(s).* **Instructions for Solving:** 1. Rewrite the exponential equation in terms of common base if possible. 2. Simplify the equation to isolate the variable \(x\). 3. Solve for \(x\) both in exact form and rounded to three decimal places. **Explanation and Steps:** When dealing with equations involving exponentials, it is often useful to express each side of the equation with the same base. In this problem, rewriting 81 as \(9^2\) might help.
### Solving Exponential Equations **Problem Statement:** Solve the following exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. \[9^{x - 6} = 81\] **Question 1: What is the exact answer?** Select the correct choice below and, if necessary, fill in the answer box to complete your choice. - **O A. The solution set is \( \{ \_\_\_\_\_\} \).** (Simplify your answer. Type an exact answer) - **O B. There is no solution.** **Question 2: What is the answer rounded to three decimal places?** Select the correct choice below and, if necessary, fill in the answer box to complete your choice. - **O A. The solution set is \( \{ \_\_\_\_\_\} \).** (Simplify your answer. Type an integer or decimal rounded to three decimal places as needed.) - **O B. There is no solution.** *Click to select and enter your answer(s).* **Instructions for Solving:** 1. Rewrite the exponential equation in terms of common base if possible. 2. Simplify the equation to isolate the variable \(x\). 3. Solve for \(x\) both in exact form and rounded to three decimal places. **Explanation and Steps:** When dealing with equations involving exponentials, it is often useful to express each side of the equation with the same base. In this problem, rewriting 81 as \(9^2\) might help.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Solving Exponential Equations
**Problem Statement:**
Solve the following exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.
\[9^{x - 6} = 81\]
**Question 1: What is the exact answer?**
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- **O A. The solution set is \( \{ \_\_\_\_\_\} \).**
(Simplify your answer. Type an exact answer)
- **O B. There is no solution.**
**Question 2: What is the answer rounded to three decimal places?**
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- **O A. The solution set is \( \{ \_\_\_\_\_\} \).**
(Simplify your answer. Type an integer or decimal rounded to three decimal places as needed.)
- **O B. There is no solution.**
*Click to select and enter your answer(s).*
**Instructions for Solving:**
1. Rewrite the exponential equation in terms of common base if possible.
2. Simplify the equation to isolate the variable \(x\).
3. Solve for \(x\) both in exact form and rounded to three decimal places.
**Explanation and Steps:**
When dealing with equations involving exponentials, it is often useful to express each side of the equation with the same base. In this problem, rewriting 81 as \(9^2\) might help.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc6811bcd-02f8-46fa-b044-8f44b9c4930d%2F7bf009c3-02e4-4b41-a14d-bd545255bde9%2Fll0hrhp.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving Exponential Equations
**Problem Statement:**
Solve the following exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.
\[9^{x - 6} = 81\]
**Question 1: What is the exact answer?**
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- **O A. The solution set is \( \{ \_\_\_\_\_\} \).**
(Simplify your answer. Type an exact answer)
- **O B. There is no solution.**
**Question 2: What is the answer rounded to three decimal places?**
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- **O A. The solution set is \( \{ \_\_\_\_\_\} \).**
(Simplify your answer. Type an integer or decimal rounded to three decimal places as needed.)
- **O B. There is no solution.**
*Click to select and enter your answer(s).*
**Instructions for Solving:**
1. Rewrite the exponential equation in terms of common base if possible.
2. Simplify the equation to isolate the variable \(x\).
3. Solve for \(x\) both in exact form and rounded to three decimal places.
**Explanation and Steps:**
When dealing with equations involving exponentials, it is often useful to express each side of the equation with the same base. In this problem, rewriting 81 as \(9^2\) might help.
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