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 log_{12}81 = p, then 3(\\frac{4 - p}{4 + p})) is equal to:

- log
_{2}8 - log
_{6}8 - log
_{4}16 - log
_{6}16

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Given, log_{12}81 = p

log_{12}(3)^{4} = p

4 (log_{12}(3)) = p

log_{12}(3) = \\frac{๐}{4}) --- (1)

We need to find the value of 3 × \\frac{4 โ p}{4 + p})

This can be rewritten as 3 × \\frac{1 โ \frac{๐}{4}}{1 + \frac{๐}{4}}) --- (2)

Replacing (2) with (1), We get

3 × \\frac{1 โ log_{12} 3}{1 + log_{12} 3})

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

3 × \\frac{log_{12} 4}{log_{12} 36})

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

log_{36}64

log_{6}8

Choice B is the correct answer.

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