Question

Which of the following is equivalent to ${\log }_{10}\left(\frac{1}{{10}^a}\right)$

• A. $-1$
• B. $-a$
• C. $a$
• D. ${10}^{-a}$
• E. ${10}^a$

Answer 1

The correct option is B $-a$

${\log }_{10}\left(\frac{1}{{10}^a}\right)={\log }_{10}1-{\log }_{10}{10}^a$

$=0-a{\log }_{10}10$

$=0-a$

$=-a$

Hence, B is the correct option.