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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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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.