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Question 12: If log1281 = p, then 3(\\frac{4 - p}{4 + p})) is equal to:

  1. log28
  2. log68
  3. log416
  4. log616

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Explanatory Answer

Method of solving this CAT Question from Logarithm

Given, log1281 = p
log12(3)4 = p
4 (log12(3)) = p
log12(3) = \\frac{๐‘}{4}) --- (1)
We need to find the value of 3 ร— \\frac{4 โ€“ p}{4 + p})
This can be rewritten as 3 ร— \\frac{1 โ€“ \frac{๐‘}{4}}{1 + \frac{๐‘}{4}}) --- (2)
Replacing (2) with (1), We get
3 ร— \\frac{1 โ€“ log_{12} 3}{1 + log_{12} 3})

3 ร— \\frac{log_{12} 12 โ€“ log_{12} 3}{log_{12} 12 + log_{12} 3})

3 ร— \\frac{log_{12} 4}{log_{12} 36})

\\frac{log_{12} 43}{log_{12} 36})

log3664
log68

Hence, the answer is log68

Choice B is the correct answer.

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