Question

Statement$-1:$ $0<x<y\Rightarrow {\log }_{a}x>{\log }_{a}y$, where $a>1$.
Statement$-2:$ When $a>1,{\log }_{a}x$ is an increasing function.

• A. Statement$-1$ is true, Statement$-2$ is true; Statement$-2$ is a correct explanation for Statement$-1$.
• B. Statement$-1$ is true, Statement$-2$ is true; Statement$-2$ is NOT a correct explanation for Statement$-1$.
• C. Statement$-1$ is true, Statement$-2$ is false.
• D. Statement$-1$ is false, Statement$-2$ is true.

Answer 1

The correct option is D Statement$-1$ is false, Statement$-2$ is true.

When $a>1,{\log }_{a}x$ is an increasing function.
$\therefore x<y\Rightarrow {\log }_{a}x<{\log }_{a}y$