CAT 2020 Quant Question [Slot 3] with Solution 01

Question

If \({\log _a}30 = A,{\log _a}(5/3) =  - B\) and \({\log _2}a = 1/3,\) then \({\log _3}a\) equals

  1. \(\frac{2}{{A + B}} - 3\)
  2. \(\frac{{A + B - 3}}{2}\)
  3. \(\frac{2}{{A + B - 3}}\)
  4. \(\frac{{A + B}}{2} - 3\)
Option: 3
Solution:

\({\log _a}5 + {\log _a}3 + {\log _a}2 = A\)

\({\log _a}5 + {\log _a}3 = A - 3\)

But \({\log _a}5 - {\log _a}3 =  - B\)

Hence \(2{\log _a}3 = A + B - 3\)

\({\log _3}a = \frac{2}{{A + B - 3}}\)

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