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\eqalign{&{155\choose0}={155\choose155} , {155\choose1}={155\choose154} , \cdots , {155\choose77}={155\choose78}\Longrightarrow\cr \Longrightarrow&{155\choose78}+{155\choose79}+\cdots+{155\choose155}=\cr &=\frac12\left({155\choose0}+{155\choose1}+\cdots+{155\choose155}\right)=\cr &=\frac122^{155}=2^{-1}2^{155}=2^{154}\Longrightarrow\cr \Longrightarrow&\log_2\left({155\choose78}+{155\choose79}+\cdots+{155\choose155}\right)=\log_22^{154}=\boxed{154}}