Question

If ${\log }_{a}x>y$ and $0<a<1$ . Then

• A. $x>y$
• B. $x>a^y$
• C. $x<a^y$
• D. $x=a^y$

Answer 1

The correct option is C

$x<a^y$

Given: ${\log }_{a}x>y$ and $0<a<1$

We know the graph of ${\log }_a$ x if $0<a<1$ is decreasing function.

If value of x increases function values decreases

If ${\log }_{a}n>y$

${\log }_{a}x>{\log }_a{a}^y$

Above given inequality is true only when

$a^y>x$