Question

What are the conditions under which the logarithm log ${}_{2x}(x^2$ - 1) is defined ?

• A. $x>0$
• B. $x>1$
• C. $x>1$ and $x<-1$
• D. $x<-1$

Answer 1

The correct option is B $x>1$

We learn that for a logarithm $lo{g}_b^a$ to be defined, the following must be satisfied.

a > 0
b > 0

Given log expression =${\log }_{2x}(x^2-1)$
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.