MathDB

Regional Olympiad - FBH 2016 Grade 11 Problem 1

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2016

September 22, 2018

algebrainequalitiesmaximum value

Problem Statement

Let

a

and

b

be real numbers bigger than

1

. Find maximal value of

c \in \mathbb{R}

such that

\frac{1}{3+\log _{a} b}+\frac{1}{3+\log _{b} a} \geq c