cat 2020 Question 21

Question

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

Accepted Answer

$2^{Y^2 (\log_3 5)} = 5^{Y^2 (\log_3 2)}$

Given,

$5^{Y^2 (\log_3 2)} = 5^{(\log_2 3)}$

⇒ $Y^2 (\log_3 2) = (\log_2 3)$

⇒ $Y^2 = (\log_2 3)^2$

⇒ $Y = (-\log_2 3)$ or $(\log_2 3)$

Since $Y$ is a negative number,

$Y = (-\log_2 3) = (\log_2 frac{1}{3})$

Question 21.