Question 42

If $$\log_{10}{11} = a$$ then $$\log_{10}{\left(\frac{1}{110}\right)}$$ is equal to

Solution

$$\log_{10}{\left(\frac{1}{110}\right)}$$

$$\log_a\left(\ \frac{\ x}{y}\right)\ =\ \log_ax-\log_ay$$

$$\log_{10}{\left(\frac{1}{110}\right)}$$ = $$=\ \log_{10}1-\log_{10}110$$

= 0$$-\log_{10}110$$

=$$-\log_{10}11\times\ 10$$

=$$-\left(\log_{10}11+\log_{10}10\right)$$

= -(a+1)

D is the correct answer.

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