### Real Analysis : Proof of a Constant

Please see the attached file for the fully formatted problem. Let > 0. Prove that log x x for x large. Prove that there exists a constant C such that log x Cx for all x 2 [1, 1 ), C ! 1 as ! 0+, and C ! 0 as ! 1 Please justify all steps and be rigorous because it is an analysis problem. (Note: The probl