Problem: Given reals , show that .
Solution: Recall the change-of-base identity for logs. We can rewrite the LHS as
Note, however that , so it remains to show that
which is true by Nesbitt’s Inequality. QED.
Comment: A good exercise in using log identities and properties to achieve a relatively simple result. Once we made the change-of-base substitution, seeing the should clue you in to Nesbitt’s. That led to the inequality , which was easily proven given the conditions of the problem.
Practice Problem: Given reals , find the best constant such that
Leave a Reply
You must be logged in to post a comment.