Explain and demonstrate how to solve the following equations for æ and how to check if your answers are correct. Part A. 52 – 6 . 5ª – 27 = 0 Part B. log,( – x + 3) + log2( – x – 5) = log2(9)

Calculus: Early Transcendentals
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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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**Title: Solving Complex Equations and Verifying Solutions**

**Explain and demonstrate how to solve the following equations for x and how to check if your answers are correct.**

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**Part A:**  
\[ 5^{2x} - 6 \cdot 5^x - 27 = 0 \]

**Part B:**  
\[ \log_2(-x + 3) + \log_2(-x - 5) = \log_2(9) \]

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**Instructions:**

1. **Part A:** Start by letting \( y = 5^x \). Transform the equation into a quadratic form and solve for \( y \). Then, revert back to solve for \( x \).

2. **Part B:** Use logarithmic properties to combine the logarithms on the left side of the equation. Solve for \( x \) by equating and simplifying expressions. 

**Check Your Answers:**

- Substitute your solutions back into the original equations to verify their correctness.
- Ensure all solutions adhere to the domain restrictions imposed by the equations, particularly those involving logarithms.
Transcribed Image Text:**Title: Solving Complex Equations and Verifying Solutions** **Explain and demonstrate how to solve the following equations for x and how to check if your answers are correct.** --- **Part A:** \[ 5^{2x} - 6 \cdot 5^x - 27 = 0 \] **Part B:** \[ \log_2(-x + 3) + \log_2(-x - 5) = \log_2(9) \] --- **Instructions:** 1. **Part A:** Start by letting \( y = 5^x \). Transform the equation into a quadratic form and solve for \( y \). Then, revert back to solve for \( x \). 2. **Part B:** Use logarithmic properties to combine the logarithms on the left side of the equation. Solve for \( x \) by equating and simplifying expressions. **Check Your Answers:** - Substitute your solutions back into the original equations to verify their correctness. - Ensure all solutions adhere to the domain restrictions imposed by the equations, particularly those involving logarithms.
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