Question

If ${\log }_{4}x<{\log }_{4}y$, then which of the following can be the possible values of $x,y$ ?

• A. $x=6,y=4$
• B. $x=4,y=2$
• C. $x=2,y=4$
• D. $x=4,y=6$

Answer 1

Answer: (C), (D)

$x=4,y=6$

Given that ${\log }_{4}x<{\log }_{4}y$
Using ${\log }_{m}x<{\log }_{m}y$
$\Rightarrow x<y,$ if $m>1$
and
$x>y,$ if $0<m<1$
Here $m>1$
So here $x<y$.
So the answer is $x=2,y=4$ and $x=4,y=6$