3. Find the smallest positive number $x$, for which the following holds: If $a, b, c, d$ are any positive numbers whose product is 1, then

$$
a^{x}+b^{x}+c^{x}+d^{x} \geqq \frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}
$$

(Pavel Novotný)