Question
If $${\log _{10}}7 = a,$$ then $${\log _{10}}\left( {\frac{1}{{70}}} \right)$$ is equal to -
Answer: Option A
$$\eqalign{
& {\log _{10}}\left( {\frac{1}{{70}}} \right) \cr
& = {\log _{10}}1 - {\log _{10}}70 \cr
& = - {\log _{10}}\left( {7 \times 10} \right) \cr
& = - \left( {{{\log }_{10}}7 + {{\log }_{10}}10} \right) \cr
& = - \left( {a + 1} \right) \cr} $$
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$$\eqalign{
& {\log _{10}}\left( {\frac{1}{{70}}} \right) \cr
& = {\log _{10}}1 - {\log _{10}}70 \cr
& = - {\log _{10}}\left( {7 \times 10} \right) \cr
& = - \left( {{{\log }_{10}}7 + {{\log }_{10}}10} \right) \cr
& = - \left( {a + 1} \right) \cr} $$
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