Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expression. Give an exact answer. Then, use a calculator to obtain approximation, correct to two decimal places, for the solution. In √√x+7=2 Rewrite the given equation without logarithms. Do not solve for x. O A. Solve the equation. What is the exact solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The solution set is {}. (Type an exact answer. Type your answer using exponential notation.) OA. The solution set is. CIE Important OB. There are infinitely many solutions. O c. There is no solution. What is the decimal approximation for the solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type an integer or a decimal rounded to two decimal places as needed.) OB. There are infinitely many solutions. OC. There is no solution. decimal

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Transcription of the Logarithmic Equation Problem**

---

**Problem Statement:**

Solve the logarithmic equation. Be sure to reject any value of \( x \) that is not in the domain of the original logarithmic expression. Give an exact answer. Then, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution.

\[
\ln \sqrt{x+7} = 2
\]

**Instructions:**

1. **Rewrite the given equation without logarithms. Do not solve for \( x \).** 

2. Solve the equation. What is the exact solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

    - **A.** The solution set is \(\{\} \).  
      *(Type an exact answer. Type your answer using exponential notation.)*
      
    - **B.** There are infinitely many solutions.
    
    - **C.** There is no solution.

3. What is the decimal approximation for the solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

    - **A.** The solution set is \(\{\} \).  
      *(Type an integer or a decimal rounded to two decimal places as needed.)*
      
    - **B.** There are infinitely many solutions.
    
    - **C.** There is no solution.

*Note: The problem has an annotation indicating 'Important' next to the first instruction. This seems to emphasize that the initial rewriting step is crucial.*

--- 

*This transcription is designed to facilitate understanding of the process of solving a logarithmic equation, reinforcing the steps to follow for an exact and approximate solution.*
Transcribed Image Text:**Transcription of the Logarithmic Equation Problem** --- **Problem Statement:** Solve the logarithmic equation. Be sure to reject any value of \( x \) that is not in the domain of the original logarithmic expression. Give an exact answer. Then, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. \[ \ln \sqrt{x+7} = 2 \] **Instructions:** 1. **Rewrite the given equation without logarithms. Do not solve for \( x \).** 2. Solve the equation. What is the exact solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. - **A.** The solution set is \(\{\} \). *(Type an exact answer. Type your answer using exponential notation.)* - **B.** There are infinitely many solutions. - **C.** There is no solution. 3. What is the decimal approximation for the solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. - **A.** The solution set is \(\{\} \). *(Type an integer or a decimal rounded to two decimal places as needed.)* - **B.** There are infinitely many solutions. - **C.** There is no solution. *Note: The problem has an annotation indicating 'Important' next to the first instruction. This seems to emphasize that the initial rewriting step is crucial.* --- *This transcription is designed to facilitate understanding of the process of solving a logarithmic equation, reinforcing the steps to follow for an exact and approximate solution.*
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