CAT 2018 Question Paper Shift 1 Solved Paper

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Question : 85 of 100

Marks: +1, -0

If

\log_{12}

81 = p , then 3

({4-p}/{4+p})

is equal to

$log_2$ 8
$log_4$ 16
$log_6$ 16
$log_6$ 8

Solution:

\log _{12} 81= {p} ⇒ \log _{12} 3^{4}= {p}

⇒ 4 \log _{12} 3= {p}

⇒ \;{ {p}}/{4}=\log _{12} 3

3(\;{4- {p}}/{4+ {p}})=3(\;{1-{ {p}}/{4}}/{1+\;{ {p}}/{4}})

=3(\;{1-\log _{12} 3}/{1+\log _{12} 3})

=3(\;{\log _{12} 12-\log _{12} 3}/{\log _{12} 12+\log _{12} 3})

=3(\;{\log (12 {/} 3)}/{\log (12 {/} 3)})

=3 \;{\log 4}/{\log 36}=3 \log _{36} 4

=\log _{6} 8

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