12. In Example 5(b), we compared the functions √log x andlog√x. Show that these functions take the same valuefor x = 10,000.

Answered: In Example 5(b), we compared the…

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

12. In Example 5(b), we compared the functions √log x and
log√x. Show that these functions take the same value
for x = 10,000.

Expert Solution

Step 1

What is Logarithmic Function:

In mathematics, the opposite of exponentiation is the logarithm. This means that the logarithm of a fixed number, base b, represents the exponent to which that fixed number must be raised in order to create a particular number x. In the simplest case, the logarithm records how many times the same factor appears throughout repeated multiplication. The notion that the logarithm is the opposite of exponentiation is also applicable to other mathematical systems. But in contexts, the logarithm frequently has various values.

Given:

Two functions $\sqrt{\log x} and \log \sqrt{x}$ are given.

To Determine:

We prove that the two functions take same value at $x = 10000$ .