This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND:
OR:
NO:

Found problems: 1

2011 District Olympiad, 4
Tags: logarithm , algebra , a implies b
[b]a)[/b] Show that , if $ a,b>1 $ are two distinct real numbers, then $ \log_a\log_a b >\log_b\log_a b. $ [b]b)[/b] Show that if $ a_1>a_2>\cdots >a_n>1 $ are $ n\ge 2 $ real numbers, then $$ \log_{a_1}\log_{a_1} a_2 +\log_{a_2}\log_{a_2} a_3 +\cdots +\log_{a_{n-1}}\log_{a_{n-1}} a_n +\log_{a_n}\log_{a_n} a_1 >0. $$