CAT 2018 Question Paper | Quants Slot 1

CAT Questions

The Quantitative Ability section of the CAT Exam has a very vast syllabus and Logarithms is one tough topic among all. From the CAT Previous Year Paper we can infer that some of the toughest questions are asked from this very topic. Here is a question from CAT 2018 Question Paper from Slot 1, based on Logarithms.. Solve this question and prepare yourself to nail the CAT Exam

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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Video Explanation

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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{𝑝}{4}) --- (1)
We need to find the value of 3 × \\frac{4 – p}{4 + p})
This can be rewritten as 3 × \\frac{1 – \frac{𝑝}{4}}{1 + \frac{𝑝}{4}}) --- (2)
Replacing (2) with (1), We get
3 × \\frac{1 – log_{12} 3}{1 + log_{12} 3})

3 × \\frac{log_{12} 12 – log_{12} 3}{log_{12} 12 + log_{12} 3})

3 × \\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.