CAT 2018 Question Paper Shift 2 Solved Paper

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Question : 83 of 100

Marks: +1, -0

If

p^3

=

q^4

=

r^5

=

s^6

, then the value of

\log_s (pqr)

is equal to

1
${24}/5$
${16}/5$
${47}/{10}$

Solution:

Let

p^{3}=q^{4}=r^{5}=s^{6}=k

p=k^{1 {/} 3}, q=k^{1 {/} 4}, r=k^{1 {/} 5}, s=k^{1 {/} 6}

{pqr}= {k}^{(\;{20+15+12}/{60})}= {k}^{\;{47}/{60}}

\log _{s}( {pqr})=\log _{ {k}^{\;{4}/{6}}} {k}^{\;{47}/{60}}

=(\;{47}/{60} × 6) \log _{ {k}} {k}

=\;{47}/{10}

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