Question

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

• A. \(-a\)
• B. \((1 + a)^{-1}\)
• C. \(\frac{1}{10a}\)
• D. \(-(a + 1)\)

Answer 1

The Correct Option is D

Step 1: Take \(a=\log_{10}11\approx 1.0414\).
Step 2: \(\log_{10}(1/110) = -\log_{10}(110) \approx -2.0414\).
Step 3: Option D gives \(-(a+1)\approx -2.0414\), an exact match; the other options give \(-1.0414\), \(0.49\), and \(0.096\), none of which match.
\[ \boxed{-(a+1)} \]