Question

If $x=lo{g}_{3}5,y=lo{g}_{17}25$, which one of the following is correct?

• A. x<y
• B. x=y
• C. x>y
• D. None of these

Answer 1

The correct option is C x>y

$y=2lo{g}_{17}5$ $\therefore \frac{1}{y}=\frac{1}{2}lo{g}_{5}17$
$\frac{1}{x}=lo{g}_{5}3=\frac{1}{2}lo{g}_{5}9$
Clearly $\frac{1}{y}>\frac{1}{x}$ $\therefore x>y$