CAT 2020 Exam Shift 1 Solved Paper

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Question : 58 of 76

Marks: +1, -0

If

y

is a negative number such that

2^{y^{2} \log _{3} 5}=5^{\log _{2} 3}

, then y equals

$\log _{2}(1 / 3)$
$-\log _{2}(1 / 3)$
$\log _{2}(1 / 5)$
$-\log _{2}(1 / 5)$

Solution:

2^{y^{2} \log _{3} 5}=5^{\log _{2} 3}

(2^{\log _{3} 5})^{y^{2}}=5^{\log _{2} 3}

(5^{\log _{2} 2})^{y^{2}}=5^{\log _{2} 3}

5^{y^{2} \log _{3} 2}=5^{\log _{2} 3}

⇒ y^{2} \log _{3} 2=\log _{2} 3

y^{2}=(\log _{2} 3)(\log _{2} 3)

is negative )

y=\log _{2} 3^{-1}=\log _{2} \;{1}/{3}

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