If $${\log _{10}}7 = a,$$   then $${\log _{10}}\left( {\frac{1}{{70}}} \right)$$   is equal to

A. - (1 + a)

B. (1 + a)^-1

C. $$\frac{a}{10}$$

D. $$\frac{1}{10a}$$

Answer: Option A

Solution(By Examveda Team)

$$\eqalign{ & {\log _{10}}\left( {{1 \over {70}}} \right) \cr & = {\log _{10}}1 - {\log _{10}}70 \cr & = - {\log _{10}}\left( {7 \times 10} \right) \cr & = - \left( {{{\log }_{10}}7 + {{\log }_{10}}10} \right) \cr & = - \left( {a + 1} \right) \cr} $$