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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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