Problem

Source: Romanian National Olympiad 2017, grade x, p. 1

Tags: equations, algebra, logarithms, fractional part, Integer Part, Floor



Solve in the set of real numbers the equation $ a^{[ x ]} +\log_a\{ x \} =x , $ where $ a $ is a real number from the interval $ (0,1). $ $ [] $ and $ \{\} $ denote the floor, respectively, the fractional part.