Let $x$ and $y$ be positive real numbers such that $\log _5(x+y)+\log _5(x-y)=3$, and $\log _2 y-\lo

Question

Let $x$ and $y$ be positive real numbers such that $\log _5(x+y)+\log _5(x-y)=3$, and $\log _2 y-\log _2 3$. Then $x y$ is equal to

Professor PC Thomas Classes · Answer

$\log_5(x^2-y^2) = 3 \Rightarrow x^2-y^2 = 125$. $\log_2 y = \log_2 3 	imes \dots$ resolves to specific roots yielding $xy = 150$.