Question

Solve the following system of equations.
$lo{g}_3\left(xy\right)=3,$
$lo{g}_{1/3}\left(x/y\right)=1.$

Answer 1

${\log }_{3}xy=3$

$⟹xy=3^3=27$

${\log }_{1/3}\left(x/y\right)=1$

$⟹\frac{x}{y}=\frac{1}{3}$

$xy.\frac{x}{y}=27.\frac{1}{3}$

$⟹x^2=9$

$⟹x=3$

$y=3x⟹y=9$

Hence , solution is $x=3,y=9$