CAT 2020 Exam Shift 3 Solved Paper

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Question : 59 of 76

Marks: +1, -0

If

a, b, c

are non-zero and

14^{a}=36^{b}=84^{\;\text "t "\;}

, then

6 b(\;{1}/{c}-\;{1}/{a})

is equal to

Your Answer:

Solution:

Let

14^{2}=36^{b}=84^{c}=k

⇒ a=\log _{14} k ⇒ \;{1}/{a}=\log _{k} 14

Similarly,

\;{1}/{c}=\log _{k} 84

and

b=\log _{36} k

Required answer,

6 b(\;{1}/{c}-\;{1}/{a})=6(\log _{36} k) ×(\log _{k} 84-\log _{k} 14)

=6 × \;{\log k}/{\log 36} × \;{\log 6}/{\log k}=3

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