已知幂函数$y=f\left(x\right)$的图象过点$(\frac{1}{2},\frac{\sqrt{2}}{2})$，则${\log }_{2}f\left(2\right)$的值为  (   )

阅读材料，回答问题

材料一：2013年是海峡两岸实现直接“三通”5周年，2008年12月15日在历经59年的波折和期待之后，台湾与大陆两岸的客机、轮船和信件，历史性地跨越台湾海峡，不再绕经第三地而直接通往彼岸，基本实现直接“三通”（如下图）。这标志着海峡两岸交流更加紧密、关系更趋缓和，并为台海地区的合作、和平、和谐铺设了光明之路。

材料二：欣赏漫画：《心愿》

A. feel     B. meet    C. beef    D. deep     ____

Building a bridge across the Straits(海峡)

    On May 3rd, 2005, KMT chairman Lien Chan finished his eight-day visit to the mainland. Only two days later, another Taiwanese leader, James Song (Song Chuyu), visited the mainland again.

    Song is the chairman of the People First Party(亲民党) in Taiwan. On his nine-day trip from May 5th to 13rd, he visited Xi'an, Nanjing, Shanghai and Changsha, as well as Beijing.

    Song, 63, was born in Xiangtan, Hunan Province in 1942. He went to Taiwan with his father at the age of seven.

    On May 9th, Song went back to Xiangtan to sweep his ancestor's(祖先的) tomb.

    He also met President Hu Jintao when he arrived in Beijing on May 11th.

    Song hoped his trip could build a bridge between the two sides. "We are here to build a bridge of trust, understanding and cooperation(合作) between Taiwan and the mainland."    he said. The two parties in Taiwan both agree with the "One China"    policy and are in favor of the final unification(统一) of China.

    Things continue to get better since Lien's visit. Taiwan can now sell more fruit in the mainland. The mainland gave a pair of giant pandas to Taiwan.

    More importantly, mainland people will soon be able to travel to the beautiful island.