3. Given the function $f(x)=\left|\log _{2} x\right|$, if real numbers $a, b(a<b)$ satisfy $f(a)=f(b)$, then the range of values for $a+2014 b$ is $\qquad$ .
3. $(2015,+\infty)$.

From the given $f(a)=f(b)$, by plotting we can see
$$
\left\{\begin{array}{l}
01, \\
\log _{2} b=-\log _{2} a .
\end{array}\right.
$$

Thus, $01$, and $a b=1$. Therefore, $a+2014 b=a+\frac{2014}{a}$. Let $g(a)=a+\frac{2014}{a}$, then $g(a)$ is a decreasing function on $(0,1)$, hence $g(a)>g(1)=2015$, so the range of $a+2014 b$ is $(2015,+\infty)$.