If \log_{10}(80) = p, \log_{10}(45) = q and \log_{10}(216) = r, then what is \log_{10}(384) equal to ?

  1. A. p + q + r
  2. B. p - q + r ✓
  3. C. p - q - r
  4. D. p + q - r

Correct Answer: B. p - q + r

Explanation

Using log properties: p = 4\log 2 + 1 - \log 2 = 3\log 2 + 1. q = 2\log 3 + 1 - \log 2. r = 3\log 2 + 3\log 3. We seek \log_{10}(384) = \log_{10}(128 \times 3) = 7\log 2 + \log 3. Evaluating the option p - q + r yields (3\log 2 + 1) - (2\log 3 + 1 - \log 2) + (3\log 2 + 3\log 3) = 7\log 2 + \log 3, matching our target.

Related questions on Arithmetic

Practice more CDS Elementary Mathematics questions