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In (x + 2)- In (x + 4x + 4) + In(e*+2) =? O x+2 O 2ln(x+2) O In(x+2) O 4ln(x+2)

In (x + 2)- In (x + 4x + 4) + In(e*+2) =? O x+2 O 2ln(x+2) O In(x+2) O 4ln(x+2)

Calculus: Early Transcendentals
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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**Question: Solve the Following Expression** Simplify the following logarithmic expression: \[ \frac{1}{2} \ln (x + 2)^4 - \ln (x^2 + 4x + 4) + \ln(e^{x + 2}) = ? \] **Options:** - ○ \( x + 2 \) - ○ \( 2 \ln(x + 2) \) - ○ \( \ln(x + 2) \) - ○ \( 4 \ln(x + 2) \) **Explanation:** 1. **Simplify Each Term:** - The first term \(\frac{1}{2} \ln (x + 2)^4\): \[\frac{1}{2} \ln (x + 2)^4 = \frac{1}{2} \cdot 4 \ln (x + 2) = 2 \ln (x + 2)\] - The second term \(\ln (x^2 + 4x + 4)\): \[\ln (x^2 + 4x + 4) = \ln ((x + 2)^2) = 2 \ln (x + 2)\] - The third term \(\ln(e^{x + 2})\): \[\ln(e^{x + 2}) = x + 2\] 2. **Combine Simplified Terms:** \[ 2 \ln (x + 2) - 2 \ln (x + 2) + x + 2 \] \[ = x + 2 \] **Answer:** The correct simplification of the expression is \( x + 2 \). Therefore, the answer is: - ○ \( x + 2 \)
Transcribed Image Text:**Question: Solve the Following Expression** Simplify the following logarithmic expression: \[ \frac{1}{2} \ln (x + 2)^4 - \ln (x^2 + 4x + 4) + \ln(e^{x + 2}) = ? \] **Options:** - ○ \( x + 2 \) - ○ \( 2 \ln(x + 2) \) - ○ \( \ln(x + 2) \) - ○ \( 4 \ln(x + 2) \) **Explanation:** 1. **Simplify Each Term:** - The first term \(\frac{1}{2} \ln (x + 2)^4\): \[\frac{1}{2} \ln (x + 2)^4 = \frac{1}{2} \cdot 4 \ln (x + 2) = 2 \ln (x + 2)\] - The second term \(\ln (x^2 + 4x + 4)\): \[\ln (x^2 + 4x + 4) = \ln ((x + 2)^2) = 2 \ln (x + 2)\] - The third term \(\ln(e^{x + 2})\): \[\ln(e^{x + 2}) = x + 2\] 2. **Combine Simplified Terms:** \[ 2 \ln (x + 2) - 2 \ln (x + 2) + x + 2 \] \[ = x + 2 \] **Answer:** The correct simplification of the expression is \( x + 2 \). Therefore, the answer is: - ○ \( x + 2 \)
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