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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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