Question

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

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

Answer 1

The correct option is B

$x>a^y$

If ${\log }_{a}x>y$ and $a>1$

We know the graph of If ${\log }_{a}x$ if and $a>1$. It is an increasing function.

Given

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

It can also be written as

${\log }_{a}x>{\log }_a{a}^y$ {This is true only when a > 1}

From the above inequality

$x>a^y$