Question

What are the conditions under which the logarithm $lo{g}_{2x}(x^2-1)$ 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 = $lo{g}_{2x}(x^2-1)$
2x > 0
x > 0 ...(1)

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

This is true when -1 < x < 1.

∴ x > 1 or x < -1 ...(2)

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