If loga30 = A, loga(5/3) = -B and log2a = 1/3, then log3a equals
Explanation:
Since all the 4 options have A + B, lets add A and B.
∴ A + B = loga30 + (-loga(5/3))
= loga30 – loga(5/3) = loga(30 × 3/5)
= loga(18) = loga(2 × 32)
⇒ A + B = loga(2) + 2loga(3)
⇒ A + B = 3 + 2loga(3) [∵ log2a = 1/3 ∴ loga2 = 3]
⇒ loga(3) = (A + B - 3)/2
⇒ log3(a) = 2/(A + B - 3)
Hence, option (c).
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