A Chinese mathematical olympiad problem and its solution:

Some body had once commented: The Silicon Valley is full of IC’s — Indians and Chinese! .

(My humble opinion: Perhaps, because of the strong emphasis on math in the two countries.)

Solve the inequality:

Solution:

As , and is monotonically increasing over , the given inequality is equivalent to :

, that is,

, which in turn, equals .

Define: . Then, we have: . Clearly, is a monotonically increasing function; then we have

That is to say, .

We obtain . So the solution set is .

Do you think you can solve this problem by another method? Please let me know.

— Nalin Pithwa.