How to prove the following inequality of logarithm?
Let
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Fletcher Hays
Answered question
2022-06-24
How to prove the following inequality of logarithm? Let Suppose
Show that
Where Here we are also considering the complex root function with respect to the principle branch of logarithm.
Answer & Explanation
Jovan Wong
Beginner2022-06-25Added 23 answers
To prove what you want, we basically just need to apply the triangle inequality to your formula. I'll look at cases separately depending whether are greater than or smaller than unit magnitude. 1. If , , then so
Hence 2. If , , then
Hence 3. If , , then by symmetry with x and y and case 2 we have 4. If , , then so,