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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)

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

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Related Questions on Logarithm

If ax = by, then:

A. $$\log \frac{a}{b} = \frac{x}{y}$$

B. $$\frac{{\log a}}{{\log b}} = \frac{x}{y}$$

C. $$\frac{{\log a}}{{\log b}} = \frac{y}{x}$$

D. None of these