Question

For ${\log }_{2x}{x}^2-1$ to be defined,

• A. $x>0$
• B. $x>1$
• C. $x<-1$

Answer 1

The correct option is B $x>1$

We learn that for ${\log }_{b}a$ to be defined, the following must be satisfied:
a > 0 and b > 0.

For ${\log }_{2x}(x^2$ - 1) to be defined,
2x > 0
x > 0...(1)

Also $x^2-1>0$
(x - 1) (x + 1) > 0.

This is true when

x > 1 or x < -1.....(2)
Combining (1) and (2) we can say x > 1 is the required condition.