CAT 2020 Exam Shift 3 Solved Paper

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Question : 51 of 76

Marks: +1, -0

If

\log _{a} 30=A, \log _{a}(5 \/ 3)=-B

and

\log _{2} a=1 / 3

, then

\log _{3} a

equals

$\;{2}/{A+B}-3$
$\;{A+B-3}/{2}$
$\;{2}/{A+B-3}$
$\;{A+B}/{2}-3$

Solution:

\log _{a} 5+\log _{a} 3+\log _{a} 2=A

\log _{a} 5+\log _{a} 3=A-3

\;\text " But "\; \log _{a} 5-\log _{a} 3=-B

\;\text " Hence "\; 2 \log _{a} 3=A+B-3

\log _{3} a=\;{2}/{A+B-3}

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