CZ-SK-MO 2009 Problem 3

Find the least value of $x>0$ such that for all positive real numbers $a,b,c,d$ satisfying $abcd=1$ , the inequality $a^x+b^x+c^x+d^x\ge\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}$ is true.