What is the step by step solution to solve this? I am having hard time understanding the steps. **Problem 2: Solve the Equation for x**\[ 2 \ln(x-3) = \ln(x+5) + \ln 4 \]This is a logarithmic equation where you need to solve for the variable $ x $.Steps to solve:1. **Combine Logarithmic Terms:** The equation can be rewritten by using logarithmic properties. The right side, $\ln(x+5) + \ln 4$, can be combined into a single logarithm: \[ \ln((x+5) \cdot 4) = \ln(4(x+5)) \]2. **Set the Logarithms Equal:** Now the equation becomes: \[ 2 \ln(x-3) = \ln(4(x+5)) \]3. **Eliminate the Logarithms:** Since the bases are the same, you can set the arguments equal to each other: \[ (x-3)^2 = 4(x+5) \]4. **Expand and Simplify the Equation:** Expand and rearrange the equation to solve for $ x $.5. **Solve the Quadratic Equation:** Solve for $ x $ considering the domain constraints due to the logarithms.**Note:** Ensure that the values obtained for $ x $ satisfy the original equation’s requirements, specifically that the arguments of the logarithms are positive.

Answered: Image /qna-images/answer/d3a89502-156d-4c83-9c04-9b21baceea21.jpg

Answered: Solve the equation for X-3 2.

Math

Algebra

Solve the equation for X-3 2.

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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Equations and inequalities describe the relationship between two mathematical expressions.

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What is the step by step solution to solve this? I am having hard time understanding the steps.

**Problem 2: Solve the Equation for x**

\[ 2 \ln(x-3) = \ln(x+5) + \ln 4 \]

This is a logarithmic equation where you need to solve for the variable $ x $.

Steps to solve:

1. **Combine Logarithmic Terms:**

The equation can be rewritten by using logarithmic properties. The right side, $\ln(x+5) + \ln 4$, can be combined into a single logarithm:

\[ \ln((x+5) \cdot 4) = \ln(4(x+5)) \]

2. **Set the Logarithms Equal:**

Now the equation becomes:

\[ 2 \ln(x-3) = \ln(4(x+5)) \]

3. **Eliminate the Logarithms:**

Since the bases are the same, you can set the arguments equal to each other:

\[ (x-3)^2 = 4(x+5) \]

4. **Expand and Simplify the Equation:**

Expand and rearrange the equation to solve for $ x $.

5. **Solve the Quadratic Equation:**

Solve for $ x $ considering the domain constraints due to the logarithms.

**Note:** Ensure that the values obtained for $ x $ satisfy the original equation’s requirements, specifically that the arguments of the logarithms are positive.

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