CAT 2020 Slot 1 QA Question 9: If $y$ is a negative number such that $2^{y^2 \log_{3} 5} = 5^{\log_{2} 3}$, then $y$ equals

Question

If $y$ is a negative number such that $2^{y^2 \log_{3} 5} = 5^{\log_{2} 3}$, then $y$ equals

Accepted Answer

Write both sides with base 2 and then equate the exponents.

$5^{\log_{2} 3} = 2^{(\log_{2} 5)(\log_{2} 3)}$
$\log_{3} 5 = \dfrac{\log_{2} 5}{\log_{2} 3}$

$2^{y^2 \log_{3} 5} = 5^{\log_{2} 3}$
$\Rightarrow y^2 	imes \dfrac{\log_{2} 5}{\log_{2} 3} = (\log_{2} 5)(\log_{2} 3)$
$\Rightarrow y^2 = (\lo

If yyy is a negative number such that 2y2log⁡35=5log⁡232^{y^2 \log_{3} 5} = 5^{\log_{2} 3}2y2log3​5=5log2​3, then yyy equals