2 _10^5 + _108 \,- 1/2 _104 = ?

Answer: Option A

$$\begin{array}{rl}& 2{\log }_{10}5+{\log }_{10}8-\frac{1}{2}{\log }_{10}4\\ & ={\log }_{10}\left(5^2\right)+{\log }_{10}8-{\log }_{10}\left(4^{\frac{1}{2}}\right)\\ & ={\log }_{10}25+{\log }_{10}8-{\log }_{10}2\\ & ={\log }_{10}\left(\frac{25\times 8}{2}\right)\\ & ={\log }_{10}100\\ & =2\end{array}$$