Question

Which is greater :
${\log }_{1/3}\frac{1}{2}or{\log }_{1/2}\frac{1}{3}$

Answer 1

Let x = $lo{g}_{1/3}\frac{1}{2}=\frac{-1}{-1}lo{g}_{3}2<lo{g}_{3}3=1$
$\therefore x=1$
y = $lo{g}_{1/2}\frac{1}{3}=\frac{-1}{-1}lo{g}_{2}3>lo{g}_{2}2=1$
$\therefore y=1$
Hence y > x or $lo{g}_{1/2}\frac{1}{3}$ > $lo{g}_{2}2=1$