Question

Which of the following is the only incorrect for $0<a<1$

• A. ${\log }_{a}x<0$ iff $x>1$
• B. ${\log }_{a}x>1$ iff $0<x<a$
• C. $0<{\log }_{a}x<1$ iff $0<x<1$
• D. ${\log }_{a}x>k\Rightarrow 0<x<a^k,k\in R$

Answer 1

The correct option is C $0<{\log }_{a}x<1$ iff $0<x<1$


All are correct except $0<{\log }_{a}x<1$ iff $0<x<1$
As $0<{\log }_{a}x<1$ iff $a<x<1$