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
Related questions
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 \(\frac{1}{2}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ddd3e79-2183-4f19-9a6c-f34fe7e86737%2Fc52177ba-6c7e-4dd3-8e91-5da4d10463ea%2F2lsorbs_processed.png&w=3840&q=75)
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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