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)
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
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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![**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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7a771320-0d7f-4ede-b409-295798de5053%2F5f4c3eed-f5a1-4972-98e7-de81a81558c7%2Fdezmhv_processed.png&w=3840&q=75)
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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