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Question 12: If log1281 = p, then 3(\\frac{4 - p}{4 + p})) is equal to:
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
Choice B is the correct answer.
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