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The value of log(75/16) - 2 log(5/9) + log(32/243) is
Alog 3
B1
Clog 2
D0
Answer & Solution
Correct answer: C. log 2
1. 2 log(5/9) = log(25/81), so the middle term becomes -log(25/81).
2. Combine: log(75/16) + log(81/25) + log(32/243).
3. Multiply arguments: (75*81*32) / (16*25*243) = (75*81*32) / (16*25*243).
4. Compute numerator 75*81*32 = 194400; denominator 16*25*243 = 97200; ratio = 2; so log 2.
_Source: ICAI BoS Foundation Paper 3, Ch 1 Unit IV 'Logarithms', p.18_
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