If a and b are chosen randomly from the set consisting of numbers 1, 2, 3, 4, 5, 6 with replacement. Then the probability that lim_(x→0)[(a^x+b^x)/2]^(2/x)]=6

If a and b are chosen randomly from the set consisting of numbers 1, 2, 3, 4, 5, 6 with replacement. Then the probability that lim_(x→0)[(a^x+b^x)/2]^(2/x)]=6

Question : If a and b are chosen randomly from the set consisting of numbers 1, 2, 3, 4, 5, 6 with replacement. Then the probability that \lim _{x\rightarrow 0}\left[ \dfrac{a^{x}+b^{x}}{2}\right] ^{\dfrac{2}{x}}=6