Question
If \({\log _a}30 = A,{\log _a}(5/3) = - B\) and \({\log _2}a = 1/3,\) then \({\log _3}a\) equals
- \(\frac{2}{{A + B}} - 3\)
- \(\frac{{A + B - 3}}{2}\)
- \(\frac{2}{{A + B - 3}}\)
- \(\frac{{A + B}}{2} - 3\)
Option: 3
Solution:
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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