PROBLEM 1. Determine the function $f:(0,+\infty) \rightarrow \mathbb{R}$ with the property:

$$
f\left(\frac{x}{2015}\right) \leq \log _{2015} x \leq f(x)-1, \quad \forall x \in(0,+\infty)
$$
## PROBLEM 1.

(2p) We substitute $x$ with $2015 \cdot x$ in the given relation

(2p) and obtain $f(x) \leq 1+\log _{2015} x$

(2p) But $f(x) \geq 1+\log _{2015} x$

(1p) Therefore, $f(x)=1+\log _{2015} x$