CAT 2020 Slot 1 QA Question & Solution
AlgebraMedium
Question
If Y is a negative number such that $2^{Y^2({\log_{3}{5})}}=5^{\log_{2}{3}}$, then Y equals to:
Options
$\log_{2}(\frac{1}{5})$
$\log_{2}(\frac{1}{3})$
$-\log_{2}(\frac{1}{5})$
$-\log_{2}(\frac{1}{3})$
Solution
$2^{Y^2({\log_{3}{5})}}=5^{Y^2(\log_3 2)}$
Given, $5^{Y^2\left(\log_32\right)}=5^{\left(\log_23\right)}$
=> $Y^2\left(\log_32\right)=\left(\log_23\right)=>Y^2=\left(\log_23\right)^2$
=>$Y=\left(-\log_23\right)^{\ }or\ \left(\log_23\right)$
since Y is a negative number, Y=$\left(-\log_23\right)=\left(\log_2\frac{1}{3}\right)$