If _107 = a, then _10 ( 170 ) is equal to

Answer: Option A

$$\begin{array}{rl}& {\log }_{10}\left(\frac{1}{70}\right)\\ & ={\log }_{10}1-{\log }_{10}70\\ & =-{\log }_{10}\left(7\times 10\right)\\ & =-\left({\log }_{10}7+{\log }_{10}10\right)\\ & =-\left(a+1\right)\end{array}$$