Problem

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2017

Tags: parameterization, algebra, logarithms, inequalities



In terms of real parameter $a$ solve inequality: $\log _{a} {x} + \mid a+\log _{a} {x} \mid \cdot \log _{\sqrt{x}} {a} \geq a\log _{x} {a}$ in set of real numbers