Question

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

• A. (a) x > 0
• B. (b) x > 1
• C. (c) x > 1 and x < -1
• D. (d) x < -1

Answer 1

The correct option is B (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.