Question

Which of the following is/are true for $a>1$

• A. ${\log }_{a}x>0$ iff $x>1$
• B. ${\log }_{a}x<0$ iff $x<1$
• C. ${\log }_{a}x>1$ iff $x>a$
• D. $0<{\log }_{a}x<1$ iff $1<x<a$

Answer 1

Answer: (A), (C), (D)

The correct options are
A ${\log }_{a}x>0$ iff $x>1$
C ${\log }_{a}x>1$ iff $x>a$
D $0<{\log }_{a}x<1$ iff $1<x<a$


So, all are correct except ${\log }_{a}x<0$ iff $x<1$ as ${\log }_{a}x<0$ iff $0<x<1$