In//x2 + 1 | 1 In]x² + 1| 2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question

How do you rewrite the top expression into the bottom? If possible.

The image contains two mathematical expressions that are logarithmic functions. Here are the expressions transcribed:

1. The first expression is:
   \[
   \ln \left| \sqrt{x^2 + 1} \right|
   \]

2. The second expression is:
   \[
   \frac{1}{2} \ln \left| x^2 + 1 \right|
   \]

These expressions involve the natural logarithm function, denoted as \(\ln\), and the absolute value, indicated by the vertical bars \(| \cdot |\). The first expression includes a square root, while the second expression is a scaled logarithmic function with a multiplication factor of \(\frac{1}{2}\).
Transcribed Image Text:The image contains two mathematical expressions that are logarithmic functions. Here are the expressions transcribed: 1. The first expression is: \[ \ln \left| \sqrt{x^2 + 1} \right| \] 2. The second expression is: \[ \frac{1}{2} \ln \left| x^2 + 1 \right| \] These expressions involve the natural logarithm function, denoted as \(\ln\), and the absolute value, indicated by the vertical bars \(| \cdot |\). The first expression includes a square root, while the second expression is a scaled logarithmic function with a multiplication factor of \(\frac{1}{2}\).
Expert Solution
Step 1

Concept:

We can use property of logarithm :

ln(m) n  =  n. ln(m) 

We can convert given expression into second form with the help of given formula:

 

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