Question

If $x={\log }_{3}5$ and $y={\log }_{17}25,$ then which of the following options is CORRECT ?

• A. $x=y$
• B. $x>y$
• C. $x<y$
• D. $xy=2$

Answer 1

The correct option is B $x>y$

$x={\log }_{3}5\Rightarrow \frac{1}{x}={\log }_{5}3=\frac{1}{2}{\log }_{5}9\dots \left(1\right)$
and $y={\log }_{17}25$
$\Rightarrow \frac{1}{y}={\log }_{25}17=\frac{1}{2}{\log }_{5}17\dots \left(2\right)$
From $\left(1\right)$ and $\left(2\right)$,
$\frac{1}{y}>\frac{1}{x}$
$\therefore x>y$